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Let P be a point on parabola x ^ 2 ...

Let P be a point on parabola ` x ^ 2 = 4y ` . If the distance of P from the centre of circle ` x ^ 2 + y ^ 2 + 6x + 8 = 0 ` is minimum, then the equation of tangent at P on parabola ` x ^ 2 = 4y ` is :

A

` x + y + 1 = 0 `

B

` x + y - 1 = 0`

C

` x - y + 1 = 0`

D

` x - y - 1 = 0`

Text Solution

Verified by Experts

The correct Answer is:
A
`x^(2) = 4y " " x^(2) + y^(2) + 6x + 8 = 0`

Line through P and C must be normal
`P(2t, t^(2)) , C (-3,0)`
`x + ty = t^(3) + 2r rArr -3 + 0 = t^(3) + 2t`
`rArr " " t^(3) + 2t + 3 = 0 rArr t = - 1 rArr P(-2,1)`
Tangent at P ,
` - 2x = 2(y +1) " "rArr " " x + y + 1 =0`
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