Conic Sections

JEE Main 2025 (Online) 3rd April Evening ShiftMCQMedium📈 Topic in 17% papers+4−1

Ques. 1JEE Main 2025, 3 April (Evening Shift)

The shortest distance between the curves y2 = 8x and x2 + y2 + 12y + 35 = 0 is:

2 3 - 1
2 2 - 1
3 2 - 1
2

Answer

(2) 2 2 - 1

Solution

The circle is x2 + (y + 6)2 = 1, with centre (0, -6) and radius 1.

The shortest distance lies along the common normal, i.e. the normal to the parabola that passes through the centre.

For y2 = 8x (a = 2), the normal at (2t2, 4t) is y = -tx + 4t + 2t3. Since it passes through (0, -6),

-6 = 4t + 2t3

t3 + 2t + 3 = 0 (t + 1)(t2 - t + 3) = 0

so t = -1 (only real root) and the foot of the normal is (2, -4).

Distance from centre = (2 - 0)2 + (-4 + 6)2 = 2 2

shortest distance = 2 2 - 1

Answer: (2)

Keep practising — Conic Sections

Ques. 2JEE Main 2025, 3 April (Evening Shift)

If the four distinct points (4, 6), (-1, 5), (0, 0) and (k, 3k) lie on a circle of radius r, then 10k + r2 is equal to

Ques. 3JEE Main 2025, 3 April (Evening Shift)

If the equation of the hyperbola with foci (4, 2) and (8, 2) is 3x2 - y2 - x + y + = 0, then + + is equal to .

Ques. 4JEE Main 2025, 2 April (Morning Shift)

If S and S′ are the foci of the ellipse x218 + y29 = 1 and P be a point on the ellipse, then (SP S'P) + (SP S'P) is equal to :

3(6 + 2)
3(1 + 2)
27
9

Ques. 5JEE Main 2025, 2 April (Morning Shift)

Let the focal chord PQ of the parabola y2 = 4x make an angle of 60 with the positive x axis, where P lies in the first quadrant. If the circle, whose one diameter is PS, S being the focus of the parabola, touches the y-axis at the point (0, ), then 5 2 is equal to:

Ques. 6JEE Main 2025, 2 April (Morning Shift)

Let one focus of the hyperbola H : x2a2 - y2b2 = 1 be at ( 10, 0) and the corresponding directrix be x = 9 10. If e and l respectively are the eccentricity and the length of the latus rectum of H, then 9(e2 + l) is equal to :

Ques. 7JEE Main 2025, 2 April (Morning Shift)

The absolute difference between the squares of the radii of the two circles passing through the point (-9, 4) and touching the lines x + y = 3 and x - y = 3, is equal to .

Ques. 8JEE Main 2025, 2 April (Evening Shift)

Let the point P of the focal chord PQ of the parabola y2 = 16x be (1, -4). If the focus of the parabola divides the chord PQ in the ratio m : n, (m, n) = 1, then m2 + n2 is equal to :

Ques. 9JEE Main 2025, 2 April (Evening Shift)

If the length of the minor axis of an ellipse is equal to one fourth of the distance between the foci, then the eccentricity of the ellipse is :

3 19
316
4 17
57

Ques. 10JEE Main 2025, 29 January (Morning Shift)

Let the ellipse E1 : x2a2 + y2b2 = 1, a > b and E2 : x2A2 + y2B2 = 1, A < B have same eccentricity 1 3. Let the product of their lengths of latus rectums be 32 3 and the distance between the foci of E1 be 4. If E1 and E2 meet at A, B, C and D, then the area of the quadrilateral ABCD equals :

24 65
18 65
6 6
12 65

Ques. 11JEE Main 2025, 29 January (Morning Shift)

Two parabolas have the same focus (4, 3) and their directrices are the x-axis and the y-axis, respectively. If these parabolas intersect at the points A and B, then (AB)2 is equal to :

All Conic Sections PYQs →

PDFDownload Conic Sections PYQs as PDF Free, with answer key and a QR code to every solution — print it or study offline⬇

All JEE Main Mathematics chapters

Class 11Sets Relations and Functions Trigonometric Functions Complex Numbers and Quadratic Equations Permutations and Combinations Binomial Theorem Sequences and Series Straight Lines Conic Sections Introduction to Three Dimensional Geometry Limits and Derivatives Statistics Probability

Class 12Relations and Functions (Class 12)Inverse Trigonometric Functions Matrices Determinants Continuity and Differentiability Application of Derivatives Integrals Application of Integrals Differential Equations Vector Algebra Three Dimensional Geometry Probability (Class 12)