Find the equations of the hyperbola satisfying the given conditions Vertices (±7, 0), e = $$\dfrac{4}{3}$$

Asked by Pragya Singh | 11 months ago |  63

Solution :-

Given:

Vertices (±7, 0) and e = $$\dfrac{4}{3}$$

Here, the vertices are on the x- axis

The equation of the hyperbola is of the form

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

Since, the vertices are (± 7, 0), so, a = 7

It is given that e = $$\dfrac{4}{3}$$

$$\dfrac{c}{a}$$ = $$\dfrac{4}{3}$$

3c = 4a

Substitute the value of a, we get

3c = 4(7)

c = $$\dfrac{28}{3}$$

It is known that, a2 + b2 = c2

72 + b2 = ($$\dfrac{28}{3}$$)2

b2 = $$\dfrac{784}{9}$$ – 49

$$\dfrac{(784 – 441)}{9}$$

$$\dfrac{343}{9}$$

The equation of the hyperbola is

$$\dfrac{x^2}{49}- \dfrac{9y^2}{343}=1$$

Answered by Abhisek | 11 months ago

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