MyQuestionIcon

1

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

Parametric Equation of Parabola

PQ, RS are tw...

Question

PQ, RS are two perpendicular chords of the hyperbola $x y = c^{2} .$ If T is the centre of hyperbola, then product of the slopes of TP, TQ, TR, TS is

A

-1

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

B

1

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

C

tending to infinity

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

D

0.0

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

Open in App

Solution

The correct option is B 1
Let coordinates of P, Q, R, S be respectively.
$(c t_{1}, \frac{c}{t_{1}}), (c t_{2}, \frac{c}{t_{2}}), (c t_{3}, \frac{c}{t_{3}}), (c t_{4}, \frac{c}{t_{4}}) P Q ⊥ R S \Rightarrow (\frac{\frac{c}{t_{2}} - \frac{c}{t_{1}}}{c t_{2} - c t_{1}}) (\frac{\frac{c}{t_{4}} - \frac{c}{t_{3}}}{c t_{4} - c t_{3}}) = - 1 \Rightarrow (- \frac{1}{t_{1} t_{2}}) (- \frac{1}{t_{3} t_{4}}) = - 1 \Rightarrow t_{1} t_{2} t_{3} t_{4} = - 1$
Now product of slopes i.e., $\frac{1}{t_{1}^{2}} . \frac{1}{t_{2}^{2}} . \frac{1}{t_{3}^{2}} . \frac{1}{t_{4}^{2}} = (- 1)^{2} = 1$

Suggest Corrections

thumbs-up

0

Similar questions

P Q

R S

are two perpendicular chords of the rectangular hyperbola

x y = c^{2}

C

is the centre of the rectangular hyperbola, then the product of the slopes of

C P, C Q, C R

C S

Q. If rectangular hyperbola

x^{2} - y^{2} = 4

is converted to

x y = - c^{2}

, then the equation of tangent to the hyperbola

x y = - c^{2}

t, t

being a parameter, is :

Q. Assertion :There exists no A.P. whose three terms are

\sqrt{3}, \sqrt{5}

\sqrt{7}

t_{p}, t_{q}

t_{r}

are three distinct terms of an A.P., then

\frac{t_{r} - t_{p}}{t_{q} - t_{p}}

is a rational number.

Q. The locus of the foot of the perpendicular from the centre of the hyperbola

x y = c^{2}

on a variable tangent is :

Q. The locus of the poles of the normal chords of the rectangular hyperbola

x y = c^{2}

View More

Join BYJU'S Learning Program

similar_icon

Related Videos

lock

Parametric Representation

MATHEMATICS

Watch in App

explore_more_icon

Explore more

Parametric Equation of Parabola

Standard XII Mathematics

Join BYJU'S Learning Program

CrossIcon