The point of the contact of the tangent to the parabola y2 = 4ax which makes an angle of 30° with X-axis, is

Question

The point of the contact of the tangent to the parabola y2 = 4ax which makes an angle of 30° with X-axis, is (A) (3a, 2√3a) (B) ( 2√3a, 3a) (C) ( √3a, 6a) (D) None of these

Tardigrade Admin · Accepted Answer

We have, slope of tangent = tan 30°=(1/√3) Now, the equation of tangent at (h, k) to y2=4 a x is y k=2 a(x+h) On comparing the slopes, we get (2 a/k) =(1/√3) or k =2 √3 a and h =3 a ∴ (h, k)=(3 a, 2 √3 a)

Q. The point of the contact of the tangent to the parabola $y^{2} = 4 a x$ which makes an angle of $3 0^{\circ}$ with $X$ -axis, is

$(3 a, 23 a)$

$(23 a, 3 a)$

$(3 a, 6 a)$

None of these

We have, slope of tangent $= tan 3 0^{\circ} = \frac{1}{3}$
Now, the equation of tangent at $(h, k)$ to $y^{2} = 4 a x$ is $y k = 2 a (x + h)$
On comparing the slopes, we get
$\frac{2 a}{k} = \frac{1}{3}$
or $k = 23 a$
and $h = 3 a$
$∴ (h, k) = (3 a, 2 3 a)$

Q. The point of the contact of the tangent to the parabola y2=4ax which makes an angle of 30∘ with X-axis, is

(3a,23​a)

(23​a,3a)

(3​a,6a)