First slide

Parabola

Question

$If line y = x + 2 do not intersect any member of family of parabolas y^{2} = α x (a \in R^{+}) at$ two distinct points, then maximum value of latus rectum is

Moderate

A

4
B

8
C

16
D

32

Solution

$y = m x + \frac{a}{m} is the equation of tangent. comparing with y = x + 2$
$m = 1 & \frac{a}{m} = 2$
$\Rightarrow m = 1, a = 2$
$∴ Latus rectum m = 4 a = 8$

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