Find the coordinates of the foci and the vertices, the eccentricity and the length of the latus rectum of the hyperbolas.9y2 – 4x2 = 36

Asked by Pragya Singh | 11 months ago |  86

Solution :-

The equation is 9y2 – 4x2 = 36 or

$$\dfrac{y^2}{2^2}- \dfrac{x^2}{3^2}=1$$

On comparing this equation with the standard equation of hyperbola

$$\dfrac{x^2}{a^2}$$ +$$\dfrac{y^2}{b^2}$$ = 1,

We get a = 2 and b = 3,

It is known that, a2 + b2 = c2

So,

c2 = 4 + 9

c2 = 13

c = $$\sqrt{13}$$

Then,

The coordinates of the foci are (0,$$\sqrt{13}$$) and (0, –$$\sqrt{13}$$).

The coordinates of the vertices are (0, 2) and (0, – 2).

Eccentricity, e = $$\dfrac{c}{a}$$$$\dfrac{\sqrt{13}}{2}$$

Length of latus rectum = $$\dfrac{2b^2}{a}$$

$$\dfrac{(2×3^2)}{2}$$

$$\dfrac{(2×9)}{2}$$

$$\dfrac{18}{2}$$

= 9

Answered by Abhisek | 11 months ago

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