Question

Find the equation to the tangents to the parabola $y^2=9x$ which goes through the point $(4,10)$

Answer 1

Equation of tangent to parabola $y^2=9xisy=mx+\frac{9}{4m}$
Since it passes through (4, 10)
$\therefore 10=4m+\frac{9}{4m}\Rightarrow 16m^2-40m+9=0$
$m=\frac{1}{4},\frac{9}{4}$
$\therefore$ equation of tangent's are $y=\frac{x}{4}+9$ & $y=\frac{9}{4}x+1$