Conic Sections

JEE Main 2024 (Online) 27th January Evening ShiftMCQMedium📈 Topic in 47% papers+4−1

Ques. 1JEE Main 2024, 27 January (Evening Shift)

Let e1 be the eccentricity of the hyperbola x216- y29=1 and e2 be the eccentricity of the ellipse x2a2+ y2b2=1, a>b, which passes through the foci of the hyperbola. If e1e2=1, then the length of the chord of the ellipse parallel to the x-axis and passing through (0,2) is :

8 53
3 5
4 5
10 53

Answer

(4) 10 53

Solution

Hyperbola: e1= 1+ 916= 54, foci ( 5,0)

e2= 1e1= 45; ellipse through ( 5,0) a=5

b2=a2 (1-e22 )=25 925=9 x225+ y29=1

[figure]

y=2: x225=1- 49= 59 x= 5 53

∴ PQ= 10 53

Answer: (4)

Keep practising — Conic Sections

Ques. 2JEE Main 2024, 27 January (Evening Shift)

Consider a circle (x- )2+(y- )2=50, where , >0. If the circle touches the line y+x=0 at the point P, whose distance from the origin is 4 2, then ( + )2 is equal to .

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