SATHEE: Hyperbola 1 Question 3

Hyperbola 1 Question 3

4.

If the vertices of a hyperbola be at $(- 2, 0)$ and $(2, 0)$ and one of its foci be at $(- 3, 0)$ , then which one of the following points does not lie on this hyperbola?

(a) $(2 \sqrt{6}, 5)$

(b) $(6, 5 \sqrt{2})$

(d) $(- 6, 2 \sqrt{10})$

(2019 Main, 12 Jan I)

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Answer:

Correct Answer: 4. (b)

Solution:

The vertices of hyperbola are given as $(\pm 2, 0)$ and one of its foci is at $(- 3, 0)$ .

$∴ (a, 0) = (2, 0)$ and $(- a e, 0), = (- 3, 0)$

On comparing $x$ -coordinates both sides, we get

$\Rightarrow a = 2$ and $- a e = - 3$

$\Rightarrow 2 e = 3 \Rightarrow e = \frac{3}{2}$

Also, $\frac{9}{4} = 1 + \frac{b^{2}}{4} \Rightarrow b^{2} = 5$

$∵ e^{2} = 1 + \frac{b^{2}}{a^{2}}$

So, equation of the hyperbola is

$\frac{x^{2}}{4} - \frac{y^{2}}{5} = 1$

The point $(6, 5 \sqrt{2})$ from the given options does not satisfy the above equation of hyperbola.

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Hyperbola 1 Question 3

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