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JEE • MATHEMATICS • STRAIGHT LINES

Straight lines practice · Easy

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Showing 181-210 of 408 questions

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181 Easy
181 of 408
Analyzing +4 | -1
The locus of a point represented by x=a2(t+1t),y=a2(t−1t)  x = \frac{a}{2}\left( {\frac{{t + 1}}{t}} \right),y = \frac{a}{2}\left( {\frac{{t - 1}}{t}} \right)\; is
View answer and explanation
Correct option: D
None of these
Option D (None of these) is correct because the locus of the point is a straight line, which is not among the given options.
182 Easy
182 of 408
Analyzing +4 | -1
The equation of a straight line passing through (1,2) and having intercept of length 3 between the straight lines 3x+4y=243x + 4y = 24 and 3x  4y=123x\;4y = 12 is
View answer and explanation
Correct option: D
None of these
The correct answer is D (None of these) because after finding the equation of the line passing through (1,2) with a length of 3 intercepted between the given lines, it does not match any of the provided options.
183 Easy
183 of 408
Application +4 | -1
The line x+y=4x + y = 4 divides the line joining (−1,1)\left( { - 1,1} \right) and (5,7) in the ratio λ:1\lambda :1, then the value of λ\lambda is
View answer and explanation
Correct option: B
01-Feb
Option B (0.5) is correct because it is the ratio in which the line divides the line segment joining the two points, calculated using the section formula.
184 Easy
184 of 408
Analyzing +4 | -1
If a variable line drawn through the intersection of the lines x3+y4=1\frac{x}{3}+\frac{y}{4}=1 and x4+y3=1\frac{x}{4}+\frac{y}{3}=1, meets the coordinates axes at AA and BB, then the locus of the mid-point of ABA B, is
View answer and explanation
Correct option: A
7xy=6(x+y)7 x y=6(x+y)
Option A (7xy=6(x+y)7 x y=6(x+y)) is correct because it is the locus of the midpoint of AB, derived from the intersection of the given lines.
185 Easy
185 of 408
Application +4 | -1
Points (1,2)(1,2) and (−2,1)(-2,1) are
View answer and explanation
Correct option: C
On the opposite side of 4x+2y=14 x+2 y=1
Option C (On the opposite side of 4x+2y=14 x+2 y=1) is correct because substituting the points into the equation 4x+2y−14x+2y-1 yields opposite signs.
186 Easy
186 of 408
Application +4 | -1
A line passing through the point P(1,2)\mathrm{P}(1,2) meets the line x+y=7x+y=7 at the distance of 3 units from PP. Then the slope of this line satisfies the equation:
View answer and explanation
Correct option: B
7x2−18x+7=07 x^2-18 x+7=0
Option B (7x2−18x+7=07 x^2-18 x+7=0) is correct because the slope of the line satisfies this quadratic equation, derived from the given conditions.
187 Easy
187 of 408
Application +4 | -1
If the lines x+3y−9=0,  4x+by−2=0x + 3y - 9 = 0,\;4x + by - 2 = 0 and 2x−y−4=02x - y - 4 = 0 are concurrent, then b equals
View answer and explanation
Correct option: A
-5
Option A (-5) is correct because the determinant of the coefficients must be zero for concurrent lines.
188 Easy
188 of 408
Application +4 | -1
The straight lines ax+by=c,  bx+cy=aax + by = c,\;bx + cy = a and cx+ay=bcx + ay = b are concurrent, if
View answer and explanation
Correct option: D
a+b+c=0a + b + c = 0
Option D (a+b+c=0a + b + c = 0) is correct because it satisfies the condition for concurrency of three lines, derived from setting the determinant of the coefficients to zero.
189 Easy
189 of 408
Application +4 | -1
The area enclosed by the lines ∣x∣+∣y∣=2|x|+|y|=2 is
View answer and explanation
Correct option: D
None of these
Option D (None of these) is correct because the area enclosed by |x| + |y| = 2 is 8 square units, which is not among the given options.
190 Easy
190 of 408
Application +4 | -1
The slopes of the lines which make an angle 45∘{45^ \circ } with the line 3x−y=−53x - y = - 5 are
View answer and explanation
Correct option: D
−2,  12- 2,\;\frac{1}{2}
Option A (x+2y−3=0x + 2y - 3 = 0) is correct because it represents a line parallel to the given lines and divides the distance between them in the specified ratio.
191 Easy
191 of 408
Application +4 | -1
The coordinate of the foot of perpendicular from (a,0) on the line y=mx+amy = mx + \frac{a}{m} are
View answer and explanation
Correct option: A
(0,am)\left( {0,\frac{a}{m}} \right)
Option A (0,am)\left( {0,\frac{a}{m}} \right) is correct because it represents the foot of the perpendicular from (a,0) to the given line, found by solving the equations of the two lines.
192 Easy
192 of 408
Application +4 | -1
Area of polygon having sides y−x−1=0,2y−2x+2=0,y−2x−2=0y-x-1=0,2 y-2 x+2=0, y-2 x-2=0 and 3y−6x−9=03 y-6 x-9=0
View answer and explanation
Correct option: D
2
Option D, 2, is the correct area of the parallelogram formed by the given lines, calculated using the formula for the area of a parallelogram formed by two pairs of parallel lines.
193 Easy
193 of 408
Application +4 | -1
Distance between lines represented by x2+22xy+2y2+4x+42y+1=0x^2+2 \sqrt{2} x y+2 y^2+4 x+4 \sqrt{2} y+1=0
View answer and explanation
Correct option: B
2
The distance between the lines is 2 because the given equation represents a pair of parallel lines, and the distance is calculated using the formula for distance between parallel lines.
194 Easy
194 of 408
Application +4 | -1
Angles made with the xx-axis by two lines drawn through the point (1,2)(1,2) and cutting the line x+y=4x+y=4 at a distance 63\frac{\sqrt{6}}{3} from the point (1,2)(1,2) are
View answer and explanation
Correct option: C
π/12\pi / 12 and 5π/125 \pi / 12
Option C (π/12\pi / 12 and 5π/125 \pi / 12) is correct because these angles satisfy the condition that the lines cut x+y=4 at a distance of 63\frac{\sqrt{6}}{3} from (1,2).
195 Easy
195 of 408
Application +4 | -1
Two points (a,0) and (0,b) are joined by a straight line. Another point on this line, is
View answer and explanation
Correct option: A
(3a,−2b)\left( {3a, - 2b} \right)
Option A ((3a,−2b)\left( {3a, - 2b} \right)) is correct because it satisfies the equation of the line joining the points (a, 0) and (0, b).

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196 Easy
196 of 408
Analyzing +4 | -1
The points A(2a,  4a),  B(2a,  6a)A\left( {2a,\;4a} \right),\;B\left( {2a,\;6a} \right) and C(2a+3a,  5a),  a>0C\left( {2a + \sqrt 3 a,\;5a} \right),\;a > 0 are the vertices of
View answer and explanation
Correct option: C
An acute angled triangle
Option C (An acute angled triangle) is correct because the triangle is equilateral, and equilateral triangles are acute angled.
197 Easy
197 of 408
Understanding +4 | -1
Distance between P(x1,y1)P\left(x_1, y_1\right) and Q(x2,y2)Q\left(x_2, y_2\right) when PQP Q is parallel to yy-axis is
View answer and explanation
Correct option: D
∣y1−y2∣\left|y_1-y_2\right|
Option D (∣y1−y2∣\left|y_1-y_2\right|) is correct because when PQ is parallel to the y-axis, the distance is the absolute difference of the y-coordinates.
198 Easy
198 of 408
Application +4 | -1
Points (8,2),(−2,−2)(8,2),(-2,-2) and (3,0)(3,0) are the vertices of
View answer and explanation
Correct option: D
None of these
Option D (None of these) is correct because the points are collinear, meaning they lie on the same line and do not form a triangle.
199 Easy
199 of 408
Application +4 | -1
The distance of the point (2,3)(2,3) from the line 2x−3y+9=02 x-3 y+9=0 measured along the line x−y+1=0,x-y+1=0, is
View answer and explanation
Correct option: D
424 \sqrt{2}
Option D (424 \sqrt{2}) is correct because it is the distance calculated along the line x−y+1=0x-y+1=0 from the point (2,3) to the line 2x−3y+9=02x-3y+9=0.
200 Easy
200 of 408
Application +4 | -1
The equation of the line with gradient −3/2- 3/2 which is concurrent with the lines 4  x+3  y−7=04\;x + 3\;y - 7 = 0 and 8  x+5  y−1=08\;x + 5\;y - 1 = 0 is
View answer and explanation
Correct option: A
3  x+2  y−2=03\;x + 2\;y - 2 = 0
The correct answer is A (3x + 2y - 2 = 0) because it represents a line with the given gradient that passes through the intersection of the two given lines.
201 Easy
201 of 408
Understanding +4 | -1
If the two vartiables xx and yy have a perfect correction (direction indirect), then they may be connected by a relation of the type
View answer and explanation
Correct option: C
xa+yb=1\frac{x}{a}+\frac{y}{b}=1
Option C (xa+yb=1\frac{x}{a}+\frac{y}{b}=1) is correct because it represents a linear relationship with a negative slope, indicating an indirect correlation.
202 Easy
202 of 408
Analyzing +4 | -1
If the points (a1,b1),(a2,b2)\left( {{a_1},{b_1}} \right),\left( {{a_2},{b_2}} \right) and (a3,b3)\left( {{a_3},{b_3}} \right) are collinear, then lines aix+biy+1=0{a_i}x + {b_i}y + 1 = 0 for aix+biy+1=0{a_i}x + {b_i}y + 1 = 0 are
View answer and explanation
Correct option: A
Concurrent
Option A (Concurrent) is correct because the collinearity of the points implies that the determinant formed by their coordinates is zero, which is also the condition for concurrency of the given lines.
203 Easy
203 of 408
Application +4 | -1
The distance of the point (-2,3) from the line x-y=5 is
View answer and explanation
Correct option: A
525\sqrt 2
Option A (525\sqrt 2) is correct because the distance is calculated using the point-to-line distance formula.
204 Easy
204 of 408
Application +4 | -1
The straight line y=x−2y=x-2 rotates about a point where it cuts the x-axis and becomes perpendicular to the straight line ax+by+c=0.ax+by+c=0. Then its equation is
View answer and explanation
Correct option: D
ay−bx+2b=0a y-b x+2 b=0
Option D (ay−bx+2b=0a y-b x+2 b=0) is correct because the new line is perpendicular to the given line and passes through the intersection point with the x-axis.
205 Easy
205 of 408
Application +4 | -1
If non-zero numbers a,b,c are in HP, then the straight line xa+yb+1c=0\frac{x}{a} + \frac{y}{b} + \frac{1}{c} = 0 always passes throught a fixed point.That point is
View answer and explanation
Correct option: B
(1,  −2)\left( {1,\; - 2} \right)
Option B ((1,  −2)\left( {1,\; - 2} \right)) is correct because it satisfies the condition derived from the harmonic progression.
206 Easy
206 of 408
Application +4 | -1
The straight line whose sum of the intercepts on the axes is equal to half to the product of the intercepts, passes through the point whose coordinates are
View answer and explanation
Correct option: B
(2,2)
Option B (2,2) is correct because the given condition leads to the equation of a line that passes through the point (2,2).
207 Easy
207 of 408
Analyzing +4 | -1
If O′(4,  8/3)O'\left( {4,\;8/3} \right) is the orthocentre of the triangle ABCABC the coordinates of whose vertices are O(0,0),A(8,0)O\left( {0,0} \right),A\left( {8,0} \right) and B(4,6),B\left( {4,6} \right), then the coordinates of the orthocentre of Δ  O′AB\Delta \;O'AB are
View answer and explanation
Correct option: A
(0,  0)\left( {0,\;0} \right)
Option A ((0, 0)) is correct because if O' is the orthocenter of triangle ABC, then O, A, B, and O' are such that each point is the orthocenter of the triangle formed by the remaining three points.
208 Easy
208 of 408
Understanding +4 | -1
The point of intersection of the lines represented by equation 2(x+2)2+3(x+2)(y−2)−2(y−2)2=02(x+2)^2+3(x+2)(y-2)-2(y-2)^2=0 is
View answer and explanation
Correct option: C
(−2,2)(-2,2)
Option C ((-2,2)) is correct because substituting X=x+2 and Y=y-2 transforms the equation to 2X²+3XY-2Y²=0, which intersects at X=0 and Y=0, thus x=-2 and y=2.
209 Easy
209 of 408
Application +4 | -1
If the points (1,3) and (5,1) are two opposite vertices of a rectangle and the other two vertices lie on the line y=2x+c,y = 2x + c,, then the value of c is
View answer and explanation
Correct option: B
-4
Option B (-4) is correct because the midpoint of the given vertices lies on the line y = 2x + c, allowing us to solve for c.
210 Easy
210 of 408
Application +4 | -1
The coordinates of the image of the origin O with respect to the line x+y+1=0x + y + 1 = 0 are
View answer and explanation
Correct option: D
(−1,−1)\left( { - 1, - 1} \right)
Option D ((-1, -1)) is correct because it is the image of the origin calculated using the formula for the image of a point with respect to a line.
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