Question

The equation of the tangent to the parabola $y^2=8x$ inclined at ${30}^{\circ }$ to the x axis is

• A. $3x-\sqrt{3y}+4=0$
• B. $2x–y+14=0$
• C. $2x-\sqrt{2y}+7=0$
• D. $x-\sqrt{3y}+6=0$

Answer 1

The correct option is D $x-\sqrt{3y}+6=0$

Slope of the tangent is (m) = $Tan{30}^{\circ }=\frac{1}{\sqrt{3}}$
It meets the parabola at y= 4$\sqrt{3}$,x=6
Equation of the tangent having slope $\frac{1}{\sqrt{3}}$and passing through the above points is $x-\sqrt{3y}+6=0$