Question

If the line $2x-3y+6=0$ is a tangent to the parabola $y^2$ = $4ax$ , then $a$ is equal to

• A. $\frac{4}{3}$
• B. $\frac{3}{4}$
• C. $\frac{2}{3}$
• D. $\frac{7}{4}$

Answer 1

The correct option is A $\frac{4}{3}$

Given,

$y^2=4ax$........(1)

$2x-3y+6=0$

$y=\frac{2}{3}x+2$......(2) $y=mx+c$

condition for straight line to touch the parabola,

$(mc-2a{)}^2=m^2{c}^2$

$\Rightarrow c=\frac{a}{m}$

$2=\frac{a}{\frac{2}{3}}$

$\frac{2\times 2}{3}=a$

$\therefore a=\frac{4}{3}$