Conic Sections

JEE Main 2024 (Online) 27th January Morning ShiftMCQEasy📈 Topic in 38% papers+4−1

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

Four distinct points (2k,3k),(1,0),(0,1) and (0,0) lie on a circle for k equal to :

Answer

(3) 513

Solution

AOB=90 AB is a diameter of the circle through O, A, B

[figure]

Circle: x(x-1)+y(y-1)=0, i.e. x2+y2-x-y=0

(2k,3k) on it: 13k2-5k=0 k=0 or 513

k=0 gives (0,0) again (points are distinct) k= 513

Answer: (3)

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Ques. 2JEE 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

Ques. 3JEE 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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