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Find the number of distinct normals that...

Find the number of distinct normals that can be drawn from `(-2,1)` to the parabola `y^2-4x-2y-3=0`

A

1

B

2

C

3

D

0

Text Solution

Verified by Experts

The correct Answer is:
A
Given parabola is
`y^(2)-2y=4x+3`
`rArr y^(2)-2y +1=4x+4`
`rArr (y-1)^(2)=4(x+1)`
`rArr y^(2)=4X, Y=y-1`
`X=x+1`
Axis is `Y=0`
`rArr y-1=0`
Also the point (-2,1) lies on the axis,
And `1+8-2-3=2 gt 0`
Point lies exterior to the parabola
`rArr` Thus only one normal is possible.
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