The equation of the tangent to the parabola \(y^2=8 x\) inclined at \(30^{\circ}\) to the \(X\)-axis is
The equation of the tangent to the parabola \(y^2=8 x\) inclined at \(30^{\circ}\) to the \(X\)-axis is
\(3 x-\sqrt{3 y}+14=0\)
\(2 x-3 y+14=0\)
\(2 x-\sqrt{3} y+7=0\)
\(x-\sqrt{3 y}+6=0\)
Solution
The equation of tangent to the parabola \(y^2=8 x\) having slope \(m=\tan \theta\) is
\(y=m x+\frac{a}{m}\)
So, the equation of required tangent is
\(y=\frac{1}{\sqrt{3}} x+\frac{2}{1 / \sqrt{3}} \Rightarrow x-\sqrt{3} y+6=0\)
Hence, option (d) is correct.