First slide

Parabola

Question

The number of distinct normals that can be drawn from (-2, 1) to the parabola $y^{2} - 4 x - 2 y - 3 = 0 is$

Moderate

A

1
B

2
C

3
D

0

Solution

$We have y^{2} - 2 y + 1 = 4 (x + 1)$
$\Rightarrow (y - 1)^{2} = 4 (x + 1)$
$Equation of axis is y - 1 = 0$
$Also (- 2, 1) lies on the axis and it is exterior to the parabola.$
$∵ 1^{2} - 4 (- 2) - 2 (1) - 3 = 1 + 8 - 5 = 4 > 0$
Hence only one normal is possible.

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