Question

The point of the contact of the tangent to the parabola $y^2=4ax$ which makes an angle of ${30}^o$ with $X$-axis, is

• A. $(3a,2\sqrt{3}a)$
• B. $(2\sqrt{3}a,3a)$
• C. $(\sqrt{3}a,6a)$
• D. None of these

Answer 1

Answer: (A)

$(3a,2\sqrt{3}a)$

We have, slope of tangent $=\tan {30}^o=\frac{1}{\sqrt{3}}$
Now, the equation of tangent at $(h,k)$ to $y^2=4ax$
is $yk=2a(x+h)$.
On comparing the slopes, we get
$\frac{2a}{k}=\frac{1}{\sqrt{3}}$
or $k=2\sqrt{3}a$
and $h=3a$
$\therefore (h,k)=(3a,2\sqrt{3}a)$