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JEE • MATHEMATICS • PARABOLA

Parabola practice · Medium

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These sets use single-correct-answer MCQs. They do not cover every JEE Main or JEE Advanced question format and are not full-length mock papers.

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Showing 31-60 of 211 questions
31 Medium
31 of 211
Analyzing +4 | -1
The possible coordinate of the point on y2=8xy^2=8 x, which is closest from x2+(y+6)2=1\mathrm{x}^2+(\mathrm{y}+6)^2=1 is :
View answer and explanation
Correct option: A
(2,−4)(2,-4)
Option A ((2,-4)) is correct because it represents the point on the parabola closest to the given circle, found by minimizing the distance between the point on the parabola and the center of the circle.
32 Medium
32 of 211
Analyzing +4 | -1
The two parabolas y2=4x{y^2} = 4x and x2=4  y{x^2} = 4\;y intersect at a point PP, whose abscissae is not zero, such that
View answer and explanation
Correct option: C
The tangents to each curve at PP make complementary angles with the xx-axis
Option C is correct because the product of the slopes of the tangents at the point of intersection is 1, implying the angles are complementary.
33 Medium
33 of 211
Analyzing +4 | -1
If P(h,k)P(h, k) be a point on the parabola x=4y2x=4 y^2, which is nearest to the point Q(0,33)Q(0,33), then the distance of PP from the directrix of the parabola y2=4(x+y)y^2=4(x+y) is equal to
View answer and explanation
Correct option: B
6
The correct answer is B (6) because after finding the point P on the parabola closest to Q, its distance from the directrix of the transformed parabola is calculated.
34 Medium
34 of 211
Application +4 | -1
The focal distance of a point on the parabola y2=4xy^2=4 x, which lies above its axis, is 10 units. If coordinates of the point are (h,k)(h, k), then h+kh+k is equal to
View answer and explanation
Correct option: C
15
Option C (15) is correct because it is the sum of the coordinates of the point on the parabola, calculated using the focal distance formula.
35 Medium
35 of 211
Application +4 | -1
If x+y=kx+y=k is a normal to the parabola y2=12xy^2=12 x, then kk is
View answer and explanation
Correct option: B
9
Option B (9) is correct because it is the value of k for which the line x+y=k is a normal to the parabola y2=12x, derived from the normal equation.
36 Medium
36 of 211
Understanding +4 | -1
A set of the parallel chords of the parabola y2=4axy^2=4 a x have their mid-point on
View answer and explanation
Correct option: C
Any straight line parallel to the axis
Option C (Any straight line parallel to the axis) is correct because the locus of the midpoints of parallel chords of a parabola is a straight line parallel to the axis of the parabola.
37 Medium
37 of 211
Application +4 | -1
The point on the parabola y2=8xy^2=8 x at which the normal is inclined at 60∘60^{\circ} to xx-axis has the coordinates
View answer and explanation
Correct option: A
(6,−43)(6,-4 \sqrt{3})
Option A ((6,−43)(6,-4 \sqrt{3})) is correct because the point satisfies the parabola equation and the normal's inclination condition.
38 Medium
38 of 211
Application +4 | -1
A chord is drawn through the focus of the parabola y2=6xy^{2}=6 x such that its distance from the vertex of this parabola is 52\frac{\sqrt{5}}{2}, then its slope can be:
View answer and explanation
Correct option: A
52\frac{\sqrt{5}}{2}
Option A (52\frac{\sqrt{5}}{2}) is correct because it represents a possible slope of the chord passing through the focus, derived from the given conditions.
39 Medium
39 of 211
Application +4 | -1
The area of the triangle formed by the tangents drawn from (x1,y1)\left(x_1, y_1\right) to y2=4axy^2=4ax and their chord of contact, is
View answer and explanation
Correct option: B
(y12−4ax1)3/22a\frac{\left(y_1{ }^2-4 a x_1\right)^{3 / 2}}{2 a}
Option B ((y12−4ax1)3/22a\frac{\left(y_1{ }^2-4 a x_1\right)^{3 / 2}}{2 a}) is correct because it represents the area of the triangle formed by the tangents and their chord of contact, derived using geometric properties and the equation of the parabola.
40 Medium
40 of 211
Application +4 | -1
The line y=2x+cy=2 x+c is a tangent to the parabola y2=16xy^2=16 x, if c equals
View answer and explanation
Correct option: D
2
Option D (2) is correct because when the line y=2x+cy=2x+c is tangent to the parabola y2=16xy^2=16x, the value of c is 2.
41 Medium
41 of 211
Application +4 | -1
The tangents drawn at the ends of any focal chord of a parabola y2=4axy^2=4 a x intersect in the line
View answer and explanation
Correct option: D
x+a=0x+a=0
Option D ((18,−12)(18,-12)) is correct because it is the point where the normal at (2,4) intersects the parabola again.
42 Medium
42 of 211
Application +4 | -1
Number of normals drawn from the point (−2,2)(-2,2) to the parabola y2−2y−2x−1=0y^2-2 y-2 x-1=0 is
View answer and explanation
Correct option: A
One
Option A (One) is correct because the cubic equation for the slope of the normal has only one real root, indicating only one normal can be drawn.
43 Medium
43 of 211
Application +4 | -1
If PP is a point on the parabola y2=4  ax{y^2} = 4\;ax such that the subtangent and subnormal at PP are equal, then the coordinates of PP are
View answer and explanation
Correct option: A
(a,2a)\left( {a,2a} \right) or (a,−2a)\left( {a, - 2a} \right)
Option A ((a,2a)\left( {a,2a} \right) or (a,−2a)\left( {a, - 2a} \right)) is correct because the subtangent equals the subnormal only at points where the ordinate is equal to the semi-latus rectum.
44 Medium
44 of 211
Application +4 | -1
The point of intersection of the latus rectum and the axis of the parabola y2+4x+2y−8=0y^2+4 x+2 y-8=0
View answer and explanation
Correct option: A
(5/4,−1)(5 / 4,-1)
Option A (5/4, -1) is correct because the point of intersection is the focus of the parabola, found by rewriting the equation in standard form.
45 Medium
45 of 211
Application +4 | -1
Let PQ be a double ordinate of the parabola, y2=−4xy^{2}=-4 x, where P\mathrm{P} lies in the second quadrant. If R\mathrm{R} divides PQ\mathrm{PQ} in the ratio 2:12: 1 then the locus of R\mathrm{R} is :
View answer and explanation
Correct option: D
9y2=−4x9 y^{2}=-4 x
Option D (9y2=−4x9 y^{2}=-4 x) is correct because it represents the locus of point R, derived from the given parabola and the section ratio.

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46 Medium
46 of 211
Analyzing +4 | -1
Let focus of a parabola be α,β\alpha, \beta such that the lines x+y−3=0,x−y+3=0,x+2y−3=0x+y-3=0, x-y+3=0, x+2 y-3=0 and x−2y+3=0x-2 y+3=0 are tangents to the parabola, then the value of α−β\alpha-\beta is equal to
View answer and explanation
Correct option: B
1
Option B (1) is correct because the focus of the parabola is found to be (0, -1) by solving the equations of the tangents, leading to α−β=0−(−1)=1\alpha - \beta = 0 - (-1) = 1.
47 Medium
47 of 211
Application +4 | -1
Find length of focal chord of parabola y2=8xy^2=8 x which is perpendicular to line x+y=1x+y=1
View answer and explanation
Correct option: B
828 \sqrt{2}
Option B (828 \sqrt{2}) is correct because the length of the focal chord perpendicular to the given line is calculated using the formula 4acsc⁡2(θ)4a \csc^2(\theta), where θ\theta is the angle the chord makes with the x-axis.
48 Medium
48 of 211
Application +4 | -1
The focus of the parabola (y−2)2=20(x+3)(y-2)^2=20(x+3) is
View answer and explanation
Correct option: C
(2,2)(2,2)
Option C (2,2) is correct because the focus of the parabola is found by comparing the given equation with the standard equation and calculating the focus using the vertex and the value of 'a'.
49 Medium
49 of 211
Application +4 | -1
If x2+6x+20y−51=0x^2+6 x+20 y-51=0, then the axis of parabola is
View answer and explanation
Correct option: A
x+3=0x+3=0
Option A (x+3=0x+3=0) is correct because the axis of the parabola is found by completing the square and identifying the x-coordinate of the vertex.
50 Medium
50 of 211
Application +4 | -1
If the line y=mx+cy=m x+c is a tangent to the parabola y2=4a(x+a)y^2=4 a(x+a) then ma+amm a+\frac{a}{m} is equal to
View answer and explanation
Correct option: A
cc
Option A (cc) is correct because if the line y=mx+cy=m x+c is a tangent to the parabola y2=4a(x+a)y^2=4 a(x+a), then ma+amm a+\frac{a}{m} is equal to cc.
51 Medium
51 of 211
Application +4 | -1
The equation of a line touching both the parabolas y2=4xy^2=4 x and x2=−32yx^2=-32 y, is
View answer and explanation
Correct option: D
x−2y+4=0x-2 y+4=0
Option D (x−2y+4=0x-2 y+4=0) is correct because by finding the tangent to the first parabola and then applying the condition for tangency to the second parabola, we arrive at this equation.
52 Medium
52 of 211
Application +4 | -1
A triangle ABCABC of area Δ\Delta is inscribed in the parabola y2=4ax{y^2} = 4ax such that AA is the vertex and BCBC is a focal chord of the parabola. The difference of the ordinates of BB and CC is
View answer and explanation
Correct option: A
2Δa\frac{{2\Delta }}{a}
The correct answer is 2Δa\frac{{2\Delta }}{a} because it represents the difference of the ordinates of B and C, calculated using the area of the triangle and the properties of the parabola.
53 Medium
53 of 211
Application +4 | -1
The point on y2=4axy^2=4 a x nearest to the focus has its abscissa equal to
View answer and explanation
Correct option: D
0
Option D (0) is correct because the distance from any point on the parabola to the focus is minimized when the point is at the vertex.
54 Medium
54 of 211
Application +4 | -1
The equation of a tangent to the parabola y2=4axy^2=4 a x which is making an angle θ\theta with xx-axis is
View answer and explanation
Correct option: C
y=xtan⁡θ+acot⁡θy=x \tan \theta+a \cot \theta
Option C (y=xtan⁡θ+acot⁡θy=x \tan \theta+a \cot \theta) is correct because it represents the equation of a tangent to the parabola y2=4axy^2=4 a x with slope tan⁡θ\tan \theta.
55 Medium
55 of 211
Application +4 | -1
A line passing through (21,30)(21,30) and normal to the curve y=2xy=2 \sqrt{x}. If m\mathrm{m} is slope of the normal then m+6=m+6=
View answer and explanation
Correct option: A
1
Option A (1) is correct because finding the slope of the normal and adding 6 gives the correct result.
56 Medium
56 of 211
Application +4 | -1
The length of the normal of the parabola y2=4x{y^2} = 4x which subtends a right angle at the vertex is
View answer and explanation
Correct option: A
636\sqrt 3
Option A (636\sqrt 3) is correct because it is the length of the normal calculated using the given conditions and properties of the parabola.
57 Medium
57 of 211
Application +4 | -1
Set of values of m for which a chord of slope m of the circle x2+y2=4{x^2} + {y^2} = 4 touches the parabola y2=4x,{y^2} = 4x, is
View answer and explanation
Correct option: A
(−∞,−2−12)∪(2−12,∞)\left( { - \infty , - \sqrt {\frac{{\sqrt 2 - 1}}{2}} } \right) \cup \left( {\sqrt {\frac{{\sqrt 2 - 1}}{2},\infty } } \right)
Option A ((−∞,−2−12)∪(2−12,∞)\left( { - \infty , - \sqrt {\frac{{\sqrt 2 - 1}}{2}} } \right) \cup \left( {\sqrt {\frac{{\sqrt 2 - 1}}{2},\infty } } \right)) is correct because it represents the set of values of m for which the chord of the circle touches the parabola.
58 Medium
58 of 211
Application +4 | -1
If end points t1,t2t_1, t_2 of a chord satisfy the relation t1t2=1t_1 t_2=1 then chord always passes through the point if parabola is y2=4x{y}^2=4 {x}
View answer and explanation
Correct option: B
(−1,0)(-1,0)
Option B ((-1,0)) is correct because the chord always passes through the point (-1,0) when the product of the parameters of the endpoints is 1.
59 Medium
59 of 211
Application +4 | -1
The locus of the mid-point of the line segment joining the focus to a moving point on the parabola y2=4axy^2=4 a x is another parabola with directrix
View answer and explanation
Correct option: C
x=0x=0
Option C (x=0x=0) is correct because it represents the directrix of the new parabola formed by the midpoints, found by eliminating the parameter and identifying the directrix.
60 Medium
60 of 211
Application +4 | -1
The common tangent of the parabolas y2=4x{y^2} = 4x and x2=−8y{x^2} = - 8y is
View answer and explanation
Correct option: D
None of these
Option D (None of these) is correct because the common tangent equation derived does not match any of the given options.
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