Conic Sections · Question 90

JEE Main 2025 (Online) 28th January Evening ShiftMCQMedium📈 Topic in 13% papers+4−1

If the midpoint of a chord of the ellipse x29 + y24 = 1 is ( 2, 4/3), and the length of the chord is 2 3, then is:

Answer

(3) 22

Solution

Chord with midpoint (x1, y1): T = S1

2x9 + (4/3)y4 = 29 + 16/94

2x9 + y3 = 23

2x + 3y = 6

Put y = 6 - 2x3 in 4x2 + 9y2 = 36:

4x2 + (6 - 2x)2 = 36

6x2 - 12 2x = 0 x = 0 or x = 2 2

End points (0, 2) and (2 2, 23 )

Length = (2 2)2 + ( 43 )2 = 8 + 169 = 883 = 2 223

= 22

Answer: (3)

JEE Main 2025 (Online) 28th January Evening Shift

Keep practising — Conic Sections

If A and B are the points of intersection of the circle x2 + y2 - 8x = 0 and the hyperbola x29 - y24 = 1 and a point P moves on the line 2x - 3y + 4 = 0, then the centroid of PAB lies on the line:

x + 9y = 36
9x - 9y = 32
4x - 9y = 12
6x - 9y = 20

JEE Main 2025 (Online) 28th January Evening Shift

Let A and B be the two points of intersection of the line y + 5 = 0 and the mirror image of the parabola y2 = 4x with respect to the line x + y + 4 = 0. If d denotes the distance between A and B, and a denotes the area of SAB, where S is the focus of the parabola y2 = 4x, then the value of (a + d) is .

JEE Main 2025 (Online) 28th January Evening Shift

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