Test Index

Hyperbola

Section: Mathematics

© examsnet.com

Question : 95 of 98

Marks: +1, -0

The normal to a curve at

P(x, y)

x

G

. If the distance of

G

from the origin is twice the abscissa of

P

, then the curve is a

circle
hyperbola
ellipse
parabola

Solution:

Equation of normal at

P(x, y)

is

Y-y=-\;\frac{dx}{dy}(x-x)

Coordinate of

G

at

X

axis is

(X, 0)

(let)

\therefore 0-y=-\;\frac{dx}{dy}(X-x) \Rightarrow y\;\frac{dy}{dx}=X-x

\Rightarrow X=x+y\;\frac{dy}{dx} \therefore

Co-ordinate of

G\left(x+y\;\frac{dy}{dx}, 0\right)

Given distance of

G

from origin = twice of the abscissa of

P

.

as distance cannot be

-v e

, therefore abscissa

x

should be

+v e

\therefore x+y\;\frac{dy}{dx}=2x \Rightarrow y\;\frac{dy}{dx}=x \Rightarrow y dx=x dx

On Integrating

\Rightarrow \;\frac{y^2}{2}=\;\frac{x^2}{2}+c_1 \Rightarrow x^2-y^2=-2c_1

\therefore

the curve is a hyperbola

© examsnet.com

Go to Question:

Prev Question

Next Question