You visited us 1 times! Enjoying our articles? Unlock Full Access!

Equation of Normal at Given Point

If the normal...

Question

If the normal at point $(1, 2)$ on the parabola $y^{2} = 4 x$ meets the parabola again a point $(t^{2}, 2 t),$ then the value of $t$ is

1

No worries! We‘ve got your back. Try BYJU‘S free classes today!

3

No worries! We‘ve got your back. Try BYJU‘S free classes today!

- 1

No worries! We‘ve got your back. Try BYJU‘S free classes today!

- 3

Right on! Give the BNAT exam to get a 100% scholarship for BYJUS courses

Open in App

Solution

The correct option is D $- 3$
If the normal at point $P (t_{1}) = (a t_{1}^{2}, 2 a t_{1})$ on the parabola $y^{2} = 4 a x$ meets the parabola again a point $Q (t) = (a t^{2}, 2 a t),$ then
$t = - t_{1} - \frac{2}{t_{1}}$
For $y^{2} = 4 x \Rightarrow a = 1$
$P = (1, 2) \Rightarrow t_{1} = 1 ∴ t = - 1 - 2 = - 3$

Suggest Corrections

Similar questions

(1, 2)

y^{2} = 4 x

(t^{2}, 2 t)

t

(1, 2)

y^{2} = 4 x

(t^{2}, 2 t),

t

y^{2} = 4 a x

(a, 2 a)

(a t^{2}, 2 a t)

(a t_{1}^{2}, 2 a t_{1})

(a t_{2}^{2}, 2 a t_{2})

t_{1}

t_{2}

t_{3}

y^{2} = 4 x

t_{1}

t_{2}

t_{2}

t_{3}

3 t_{1} + 13 t_{2} + 9 t_{3}

t_{1}

Join BYJU'S Learning Program

Explore more

Join BYJU'S Learning Program