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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 `
`implies y^(2) -2y + 1 = 4x + 4 " "implies (y-1)^(2) =4(x+1)`
` implies Y^(2) = 4X , Y = y-1`
` X = x +1`
Axis is Y=0
`implies 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
`implies ` Thus only one normal is possible.
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