A hyperbola passes through the points (3, 2) | vedclass

Name: PDF Generator App | JEE NEET Paper Generator | Vedclass
Brand: Vedclass
Rating: 5 (35 reviews)

Question

(a) Let the equation of hyperbola is $\frac{{{x^2}}}{{{a^2}}} - \frac{{{y^2}}}{{{b^2}}} = 1$

But it passes through $(3, 2)$

==> $\frac{9}{{{a

Vedclass · Accepted Answer

$2$

Vedclass · Answer

(a) Let the equation of hyperbola is $\frac{{{x^2}}}{{{a^2}}} - \frac{{{y^2}}}{{{b^2}}} = 1$

But it passes through $(3, 2)$

==> $\frac{9}{{{a^2}}} - \frac{4}{{{b^2}}} = 1$.....$(i)$

Also its passes through $(-17, 12)$

==> $\frac{{{{( - 17)}^2}}}{{{a^2}}} - \frac{{{{(12)}^2}}}{{{b^2}}} = 1$ .....$(ii)$

Solving these, we get $a = 1$ and $b = \sqrt 2 $

Hence length of transverse axis $ = 2a = 2$.

A hyperbola passes through the points $(3, 2)$ and $(-17, 12)$ and has its centre at origin and transverse axis is along $x$ - axis. The length of its transverse axis is

Similar Questions

Find the coordinates of the foci and the vertices, the eccentricity, and the length of the latus rectum of the hyperbola $\frac{x^{2}}{16}-\frac{y^{2}}{9}=1$

Centre of hyperbola $9{x^2} - 16{y^2} + 18x + 32y - 151 = 0$ is

Find the coordinates of the foci and the vertices, the eccentricity, and the length of the latus rectum of the hyperbola $16 x^{2}-9 y^{2}=576$

Eccentricity of the rectangular hyperbola $\int_0^1 {{e^x}\left( {\frac{1}{x} - \frac{1}{{{x^3}}}} \right)} \;dx$ is

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