Equation of normal to the hyperbola $x y = c^{2}$ at the point $P (x_{1}, y_{1})$ is $x x_{1} - y y_{1} = {x_{1}}^{2} - {y_{1}}^{2} .$

True

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

False

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

Open in App

Solution

The correct option is A True

Suggest Corrections

Similar questions

If $P (x_{1}, y_{1})$ is such that $\frac{x_{1}^{2}}{a^{2}} - \frac{y_{1}^{2}}{b^{2}} > 1$ .

Then the point P situates outside the standard hyperbola $\frac{x_{1}^{2}}{a^{2}} - \frac{y_{1}^{2}}{b^{2}} >= 1$ .

The equation of the chord of the circle $x^{2} + y^{2} = a^{2}$ having $(x_{1}, y_{1})$ as its mid-point is

\frac{x^{2}}{36} - \frac{y^{2}}{25} = 1

(2, 4)

(1, 2)

T = S_{1}

(x_{1} y_{1})

\frac{x x_{1}}{a^{2}} - \frac{y y_{1}}{b^{2}} = \frac{x_{1}^{2}}{a^{2}} - \frac{y_{1}^{2}}{b^{2}}

What is the length of tangent from a point $P (x_{1}, y_{1})$ to the circle $x^{2} + y^{2} + 2 g x + 2 f y + c = 0.$

If $(x_{1}, y_{1})$ is a point inside the circle $x^{2} + y^{2} + 2 g x + 2 f y + c = 0$ Given two expressions $S_{1}$ and $T_{1}$ such that,

$S_{1} = x_{1}^{2} + {y_{1}}^{2} + 2 g x_{1} + 2 f y_{1} + c$

$T_{1} = x x_{1} + y y_{1} + g (x + x_{1}) + f (y + y_{1}) + c$

Then the equation of chord centered at $(x_{1}, y_{1})$ is

Join BYJU'S Learning Program