AP EAMCET · Maths · Parabola
The equation of the tangent to the parabola \(y^2=8 x\) inclined at \(30^{\circ}\) to the \(X\)-axis is
- A \(3 x-\sqrt{3 y}+14=0\)
- B \(2 x-3 y+14=0\)
- C \(2 x-\sqrt{3} y+7=0\)
- D \(x-\sqrt{3 y}+6=0\)
Answer & Solution
Correct Answer
(D) \(x-\sqrt{3 y}+6=0\)
Step-by-step Solution
Detailed explanation
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.
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