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Conic section PYQ series 2024

 Q. If the shortest distance of the parabola y² = 4x from the centre of the circle x² + y²– 4x- 16y + 64 = 0 is d, then d² is equal to:

 ( JEE mains 2024)

A. 16

B.  24

C. 20

D. 36

Ans:- (c)

Equation of normal to parabola

 y = mx-2m-m³

 this normal passing through center of circle (2, 8)

 8=2m-2m -m³ 

m =-2 

So point P on parabola (am², -2am) = (4, 4)

 And 

C = (2, 8)

 PC = √4+16=√20 

d² = 20

Sequence and series

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