Question

The line $y=mx+c$ will touch the parabola $x^2=4ay$ if $c$

• A. $a{m}^2$
• B. $-a{m}^2$
• C. $2am$
• D. None of these

Answer 1

The correct option is B $-a{m}^2$

Let $y=mx+c$ will touch the parabola $x^2=4ay$.

Then

$x^2=4a(mx+c)$ [The line will satisfy the given equation of parabola]

or, $x^2-4amx-4ac=0$

As the line is tangent then the discriminant of the above equation will be zero.

Then $(-4am{)}^2-4.(1).(-4ac)=0$

or, $16a^2{m}^2+16ac=0$

or, $c=-a{m}^2$.