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JEE • MATHEMATICS • PAIR OF STRAIGHT LINES

Pair of straight lines practice · Mixed difficulty

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Showing 151-180 of 264 questions

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151 Easy
151 of 264
Analyzing +4 | -1
Number of points lying on the line 7x+4y+2=07 x+4 y+2=0 which is equidistant from the lines 15x2+56xy+48y2=015 x^2+56 x y+48 y^2=0 is
View answer and explanation
Correct option: C
2
Option C (2) is correct because solving the equidistant condition yields two distinct values for λ, indicating two points on the line.
152 Easy
152 of 264
Application +4 | -1
The distance between parallel lines 8x2+8xy+2y2+26x+8 x^2+8 x y+2 y^2+26 x+ 13y+15=013 y+15=0 is
View answer and explanation
Correct option: D
7510\frac{7 \sqrt{5}}{10}
Option D (7510\frac{{7 \sqrt{{5}}}}{{10}}) is correct because it is the calculated distance between the parallel lines using the given formula.
153 Easy
153 of 264
Application +4 | -1
If Lx2−10xy+12y2+5x−16y−3=0L x^2-10 x y+12 y^2+5 x-16 y-3=0 represents a pair of straight lines, find the value of LL.
View answer and explanation
Correct option: A
2
Option A (2) is correct because it is the value of L that makes the given equation represent a pair of straight lines, derived by applying the condition abc+2fgh−af2−bg2−ch2=0abc + 2fgh - af^2 - bg^2 - ch^2 = 0.
154 Medium
154 of 264
Application +4 | -1
Which of the following pairs of straight lines intersects at right angles?
View answer and explanation
Correct option: A
2x2=y(x+2y)2 x^2=y(x+2 y)
Option A (2x2=y(x+2y)2x^2 = y(x+2y)) is correct because the sum of the coefficients of x2x^2 and y2y^2 is zero, which is the condition for lines intersecting at right angles.
155 Easy
155 of 264
Application +4 | -1
If the equation λx2+4xy+5y2=0\lambda x^2+4 x y+5 y^2=0 represents two lines inclined at an angle π\pi, then λ=\lambda=
View answer and explanation
Correct option: B
4/54 / 5
Option B (4/54 / 5) is correct because for the lines to be inclined at an angle π\pi, they must be coincident, implying h2−ab=0h^2 - ab = 0, which leads to λ=4/5\lambda = 4/5.
156 Medium
156 of 264
Application +4 | -1
The slope of a line is 3 times the slope of the other line and the tangent of the angle between them is 4/134 / 13, sum of their slopes is equal to
View answer and explanation
Correct option: D
8
Option D (8) is correct because solving the tangent of the angle between two lines equation leads to two possible values for the slopes, and one of them results in the sum of slopes being 8.
157 Easy
157 of 264
Application +4 | -1
The equation to the pair of lines perpendicular to the pair of lines 3x2−4xy+y2=03 x^2-4 x y+y^2=0, is
View answer and explanation
Correct option: A
x2+4xy+3y2=0x^2+4 x y+3 y^2=0
Option A (x2+4xy+3y2=0x^2+4 x y+3 y^2=0) is correct because the equation of the perpendicular lines is obtained by interchanging the coefficients of x2x^2 and y2y^2 and changing the sign of the middle term.
158 Easy
158 of 264
Application +4 | -1
The angle between the pair of lines 2x2+5xy+2y2+3x+3  y+1=0,2{x^2} + 5xy + 2{y^2} + 3x + 3\;y + 1 = 0, is
View answer and explanation
Correct option: A
cos⁡−1(4/5){\cos ^{ - 1}}\left( {4/5} \right)
The correct answer is A (cos⁻¹(4/5)) because the angle between the pair of lines is calculated using the formula involving the coefficients of the quadratic equation.
159 Easy
159 of 264
Application +4 | -1
If the equations, 12x2−10xy+2y2+11x−5y+k=012{x^2} - 10xy + 2{y^2} + 11x - 5y + k = 0 represents two straight lines, then the value of kk is
View answer and explanation
Correct option: B
2
Option B (2) is correct because the value of k is found by applying the condition for a general second-degree equation to represent a pair of straight lines.
160 Medium
160 of 264
Application +4 | -1
If one of the lines given by ax2+2hxy+by2=0a x^2+2 h x y+b y^2=0 bisects the angle between coordinate axes, then
View answer and explanation
Correct option: A
(a+b)2=4h2(a+b)^2=4 h^2
Option A ((a+b)2=4h2(a+b)^2=4 h^2) is correct because it represents the condition when one of the lines bisects the angle between the coordinate axes.
161 Easy
161 of 264
Application +4 | -1
The value of λ\lambda for which the equation 6x2+11xy−10y2+x+31y+λ=06 x^2+11 x y-10 y^2+x+31 y+\lambda=0 represents a pair of straight lines, is
View answer and explanation
Correct option: A
-15
Option A (-15) is correct because it satisfies the condition for the given equation to represent a pair of straight lines, where the determinant Δ=0\Delta = 0.
162 Easy
162 of 264
Application +4 | -1
If ‘θ\theta’ is the angle between the lines ax2+2hxy+by2=0,  a{x^2} + 2hxy + b{y^2} = 0,\; then angle between x2+2xysec  θ+y2=0{x^2} + 2xy\mathrm{sec\;\theta } + {y^2} = 0 is
View answer and explanation
Correct option: A
θ\theta
Option A (θ\theta) is correct because the angle between the second pair of lines simplifies to the same expression as the angle between the first pair.
163 Easy
163 of 264
Analyzing +4 | -1
Two of the straight lines given by 3x3+3x2y−3xy2+dy3=03 x^3+3 x^2 y-3 x y^2+d y^3=0 are at right angles, if dd equal to
View answer and explanation
Correct option: B
−3-3
Option B (-3) is correct because substituting the condition for perpendicular lines into the given equation yields d = -3.
164 Easy
164 of 264
Application +4 | -1
All chords of the curve 3x2−y2−2x+4y=03{x^2} - {y^2} - 2x + 4y = 0 which subtend a right angle at the origin, pass through the fix point
View answer and explanation
Correct option: B
(1,-2)
The correct answer is A (1,-2) because the equation of the chord is used to homogenize the given curve equation, and then the condition for the lines to be perpendicular is applied to find the fixed point.
165 Easy
165 of 264
Analyzing +4 | -1
The equation of line which is parallel to the line common to the pair of lines given by 3x2+xy−4y2=03 x^2+x y-4 y^2=0 and 6x2+11xy+4y2=06 x^2+11 x y+4 y^2=0 and at a distance of 2 units from it is
View answer and explanation
Correct option: C
3x+4y=103 x+4 y=10
Option C (3x+4y=103 x+4 y=10) is correct because it represents a line parallel to the common line of the given pair of lines and is at a distance of 2 units from it.

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166 Easy
166 of 264
Application +4 | -1
The value of λ\lambda such that λ\lambda x2−10xy+12y2+5x−16y−3=0{x^2} - 10xy + 12{y^2} + 5x - 16y - 3 = 0 represent a pair of straight lines, is
View answer and explanation
Correct option: C
2
Option C (2) is correct because this value of λ\lambda makes the given equation represent a pair of straight lines.
167 Easy
167 of 264
Application +4 | -1
The pair of lines 3x2−4xy+3y2=0\sqrt{3} x^2-4 x y+\sqrt{3} y^2=0 are rotated about the origin by π6\frac{\pi}{6} in the anti-clockwise sense.
The equation of the pair in the new position is
View answer and explanation
Correct option: C
3x2−xy=0\sqrt{3} x^2-x y=0
The correct answer is C (3x2−xy=0\sqrt{3} x^2-x y=0) because rotating the pair of lines by π6\frac{\pi}{6} results in the equation 3x2−xy=0\sqrt{3} x^2-x y=0.
168 Easy
168 of 264
Application +4 | -1
If the sum of the slopes of the lines given by x2+2cxy−y2=0x^2+2 c x y-y^2=0 is four times their product, then cc has the value
View answer and explanation
Correct option: A
−2-2
Option A (-2) is correct because it satisfies the condition where the sum of the slopes is four times their product for the given equation.
169 Easy
169 of 264
Understanding +4 | -1
The angle between the lines represented by x2−y2=0{x^2} - {y^2} = 0 is
View answer and explanation
Correct option: C
90∘90^\circ
Option C (90∘90^\circ) is correct because the equation x2−y2=0{x^2} - {y^2} = 0 represents two perpendicular lines.
170 Easy
170 of 264
Application +4 | -1
Two lines are given by (x−2y)2+λ(x−2y)=0(x-2 y)^2+\lambda(x-2 y)=0. The value of ∣λ∣|\lambda| so that the distance between them is 3 , is
View answer and explanation
Correct option: C
353 \sqrt{5}
The correct answer is C (353 \sqrt{5}) because the distance between the parallel lines is given as 3, and solving for ∣λ∣|\lambda| yields 353 \sqrt{5}.
171 Easy
171 of 264
Application +4 | -1
The equation of two straight lines through the point (x1,y1)\left(x_1, y_1\right) and perpendicular to the lines given by ax2+2hxy+by2=0,a x^2+2 h x y+b y^2=0, is
View answer and explanation
Correct option: A
b(x−x1)2−2h(x−x1)(y−y1)+a(y−y1)2=0b\left(x-x_1\right)^2-2 h\left(x-x_1\right)\left(y-y_1\right)+a\left(y-y_1\right)^2=0
Option A (b(x−x1)2−2h(x−x1)(y−y1)+a(y−y1)2=0b(x-x_1)^2-2 h(x-x_1)(y-y_1)+a(y-y_1)^2=0) is correct because it represents the equation of lines perpendicular to the given lines, shifted to pass through the point (x1, y1).
172 Easy
172 of 264
Application +4 | -1
The equation of pair of lines through origin and perpendicular to the pair of lines ax2+2hxy+by2=0a x^2+2 h x y+b y^2=0 is
View answer and explanation
Correct option: D
bx2−2hxy+ay2=0b x^2-2 h x y+a y^2=0
Option D (bx2−2hxy+ay2=0b x^2-2 h x y+a y^2=0) is correct because it represents the equation of a pair of lines perpendicular to the given pair of lines and passing through the origin.
173 Easy
173 of 264
Application +4 | -1
The area (in square unit) of the triangle formed by x+y+1=0x + y + 1 = 0 and the pair of straight lines x2−3xy+2y2=0{x^2} - 3xy + 2{y^2} = 0 is
View answer and explanation
Correct option: C
112\frac{1}{{12}}
Option C (112\frac{1}{{12}}) is correct because it represents the area of the triangle formed by the line and the pair of straight lines, calculated by finding the intersection points and using the area formula.
174 Easy
174 of 264
Application +4 | -1
The equation of the bisector of the angle between the straight lines 3x−4y+7=03 x-4 y+7=0 and 12x−5y−8=012 x-5 y-8=0, is
View answer and explanation
Correct option: D
21x+27y−131=021 x+27 y-131=0
Option D (21x+27y−131=021 x+27 y-131=0) is correct because it is the equation of one of the angle bisectors between the two given lines.
175 Medium
175 of 264
Application +4 | -1
One diagonal of a square is the portion of the line 3x+2y=123 x+2 y=12 intercepted between the axes. The coordinates of the extremity of the other diagonals not lying in the first quadrant are
View answer and explanation
Correct option: C
(−1,1)(-1,1)
Option C ((-1,1)) is correct because it satisfies the condition that the other diagonal's extremity lies on a line derived from the square's properties and the given diagonal.
176 Easy
176 of 264
Application +4 | -1
An equation of a straight line passing through the inter-section of the straight lines 3x−4y+1=03 x-4 y+1=0 and 5x+y−1=05 x+y-1=0 and making non-zero, equal intercepts on the axes is
View answer and explanation
Correct option: B
23x+23y=1123 x+23 y=11
Option D (4x+y=13,4x−y=74 x+y=13,4 x-y=7) is correct because these are the equations of the diagonals of the parallelogram formed by the given lines.
177 Easy
177 of 264
Application +4 | -1
The line x=ay+b,z=cy+dx=a y+b, z=c y+d and x=a′y+b′,z=c′y+d′x=a^{\prime} y+b^{\prime}, z=c^{\prime} y+d^{\prime} are perpendicular if-
View answer and explanation
Correct option: D
aa′+cc′+1=0{aa}^{\prime}+{cc}^{\prime}+1=0
Option D ({aa}^{\'}+{cc}^{\'}+1=0{aa}^{\'}+{cc}^{\'}+1=0) is correct because the lines are perpendicular if the dot product of their direction ratios is zero, leading to the given condition.
178 Medium
178 of 264
Application +4 | -1
The angle between the lines joining the origin to the points of intersection of the line 3x+y=2\sqrt{3} x+y=2 and the curve y2−x2=4y^2-x^2=4 is
View answer and explanation
Correct option: C
tan⁡−1(32)\tan ^{-1}\left(\frac{\sqrt{3}}{2}\right)
Option C (tan⁡−1(32)\tan ^{-1}(\frac{\sqrt{3}}{2})) is correct because it is obtained by homogenizing the equation and then using the formula for the angle between the lines.
179 Easy
179 of 264
Application +4 | -1
The angle between the straight lines x2−y2−2  x−1=0,{x^2} - {y^2} - 2\;x - 1 = 0, is
View answer and explanation
Correct option: A
90∘90^\circ
Option A (90∘90^\circ) is correct because the given equation represents a pair of perpendicular lines since the coefficient of x2x^2 plus the coefficient of y2y^2 equals zero.
180 Easy
180 of 264
Understanding +4 | -1
The joint equation of the straight lines x+y=1x + y = 1 and x−y=4,x - y = 4, is
View answer and explanation
Correct option: C
(x+y−1)(x−y−4)=0\left( {x + y - 1} \right)\left( {x - y - 4} \right) = 0
Option C ((x+y−1)(x−y−4)=0\left( {x + y - 1} \right)\left( {x - y - 4} \right) = 0) is correct because the joint equation is obtained by multiplying the individual equations after setting them equal to zero.
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