Tangents to the parabola& y^ 2 = 4ax at P (a t _ 1 ^ 2 , 2a t _ 1 ) and Q (a t _ 2 ^ 2 , 2a t _ 2 ) meet at T . If △ PTQ is right-angled at T, then (1)/(PS) + (1)/(QS) is equal to (where,& S is the focus of the given

Correct answer: A. (1)/(a) T lies on the directrix and PQ is the focal chord. ⇒ t _ 1 t _ 2 = - 1 (1)/(PS) = 1 a(1 + t _ 1 ^ 2 ) , (1)/(QS) = 1 a (1 + t _ 2 ^ 2 ) = t _ 1 ^ 2 a(1 + t _ 1 ^ 2 ) So, (1)/(PS) + (1)/(QS) = (1)/(a)

NTA Abhyas 2020

Exam: NTA Abhyas
Year: 2020
Subject: Mathematics
Chapter: Parabola

NTA Abhyas 2020 · Mathematics · Parabola

Tangents to the parabola& y^ 2 = 4ax at P (a t _ 1 ^ 2 , 2a t _ 1 )...

Tangents to the parabola&

y^{2} = 4ax

P \left(a{t}_{1}^{2}, 2a{t}_{1}\right)

and

Q \left(a{t}_{2}^{2}, 2a{t}_{2}\right)

meet at

T .

△ PTQ

is right-angled at

T,

then

\dfrac{1}{PS} + \dfrac{1}{QS}

is equal to (where,&

S

is the focus of the given parabola)

Options

A $\dfrac{1}{a}$
B $\dfrac{2}{a}$
C $\dfrac{1}{2a}$
D $\dfrac{1}{4a}$

Correct answer

A. $\dfrac{1}{a}$

Step-by-step solution

$T$ lies on the directrix $</p><p>and$ PQ $is the focal chord.$

$⇒ {t}_{1}{t}_{2} = - 1$
$\dfrac{1}{PS} = \dfrac{1}{a\left(1 + {t}_{1}^{2}\right)}$ , $\dfrac{1}{QS} = \dfrac{1}{a \left(1 + {t}_{2}^{2}\right)} = {t}_{1}^{2}a\left(1 + {t}_{1}^{2}\right)<br />So, \dfrac{1}{PS} + \dfrac{1}{QS} = \dfrac{1}{a}</p>$

Practice Parabola on Quantrex Academy →

More from Parabola