Number of possible tangents which can be drawn to curve 4x^2 - 9y^2 = 36 , which are perpendicular t

English

Gujarati

Hindi

10-2. Parabola, Ellipse, Hyperbola

normal

The number of possible tangents which can be drawn to the curve $4x^2 - 9y^2 = 36$ , which are perpendicular to the straight line $5x + 2y -10 = 0$ is

A

$0$

B

$1$

C

$2$

D

$4$

Solution

Slope of tangent $=\frac{2}{5}$

Now $c^{2}=a^{2} m^{2}-b^{2}$

$=9\left(\frac{2}{5}\right)^{2}-4<0$

No such tangent exist

Standard 11

Mathematics

Share

Similar Questions

Let $P \left( x _0, y _0\right)$ be the point on the hyperbola $3 x ^2-4 y ^2$ $=36$, which is nearest to the line $3 x+2 y=1$. Then $\sqrt{2}\left( y _0- x _0\right)$ is equal to :

hard

(JEE MAIN-2023)

If $4{x^2} + p{y^2} = 45$ and ${x^2} – 4{y^2} = 5$ cut orthogonally, then the value of $p$ is

hard

The length of transverse axis of the parabola $3{x^2} – 4{y^2} = 32$ is

easy

The equation of the director circle of the hyperbola $\frac{{{x^2}}}{{16}} – \frac{{{y^2}}}{4} = 1$ is given by

easy

If $e$ and $e’$ are the eccentricities of the ellipse $5{x^2} + 9{y^2} = 45$ and the hyperbola $5{x^2} – 4{y^2} = 45$ respectively, then $ee' = $

medium