If two tangents drawn from the point P ( h, k ) to the parabola y^...

Equation of tangent in slope form is $y = mx + \dfrac{a}{m}$
Let the tangent passes through $P \left(h, k\right)<br />$⇒ k = mh + $\dfrac{a}{m}$⇒ m^{2}h - km + a = 0$<br />$⇒ {m}_{1} + {m}_{2} = $\dfrac{k}{h}$& {m}_{1}{m}_{2} = $\dfrac{a}{h}<br />Where,~$a = 2 & {m}_{2} = 3{m}_{1}$<br />$⇒ 4{m}_{1} = $\dfrac{k}{h }$& $3 \left({m}_{1}\right)$2 = $\dfrac{2}{h}<br />$⇒ $3{ \left(\dfrac{k}{4h}\right)}^{2} = \dfrac{2}{h}⇒ 3y^{2} = 32x$