Q105 / 160 · AP EAMCET 2020 (21 Sep Shift 2) · Mathematics

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
\(2 x-\sqrt{3} y+7=0\)
Correct answer
D
\(x-\sqrt{3 y}+6=0\)

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.

Hence, the correct answer is option: 'D'.

Relevant Questions

Tangents are drawn at three points on the parabola . Let these tangents intersect each other at the points . If , then the area of the trian24 May, 2025 (M)Tangent to Parabola
If the perpendicular distance from the focus of a parabola to its directrix is , then the equation of the normal drawn at is22 May, 2025 (E)Tangent to Parabola
Equation of a tangent line of the parabola , which passes through the point is20 May, 2024 (E)Tangent to Parabola
and are two points on the curve . The coordinates of the point on the curve such that the tangent drawn at is parallel to the chord , is18 May, 2023 (E)Tangent to Parabola
Equation of the directrix of the parabola whose focus is ( 0 , 0 ) and the tangent at the vertex is x - y + 1 = 0 is04 Jul, 2022 (M)Tangent to Parabola
If are the parametric equations of the parabola , then the value of equals24 Aug, 2021 (M)Tangent to Parabola