If the three normals drawn to the parabola, y2 = 2x pass through the point (a, 0) a [] 0, …

Question

If the three normals drawn to the parabola, y2 = 2x pass through the point (a, 0) a $$\ne$$ 0, then 'a' must be greater than :

Accepted Answer

Let the equation of the normal is

y = mx - 2am - am3

here 4a = 2 $$ \Rightarrow $$ a = $${1 \over 2}$$

y = mx - m - $${1 \over 2}$$m3

It passing through A(a, 0) then

0 = am - m - $${1 \over 2}$$m3

m = 0, a - 1 - $${1 \over 2}$$m2 = 0

m2 = 2(a - 1) > 0

$$ \Rightarrow $$ a > 1

Solutions · 1