First slide

Parabola

Question

Distance of a point $P$ on the parabola $y^{2} = 48 x$ from
the focus is $l$ and its distance from the tangent at
the vertex is $d$ , then $l - d$ is equal to

Moderate

A

4
B

8
C

12
D

16

Solution

Any point on the parabola is $P (12 t^{2}, 24 t)$ whose
distance from the focus (12, 0) is 12( $t^{2} + 1) = t$ and
from y-axis, the tangent at the vertex is $12 t^{2} = d$ .
So $l - d = 12 .$

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