SATHEE: Hyperbola 2 Question 14

Hyperbola 2 Question 14

14.

Equation of a common tangent with positive slope to the circle as well as to the hyperbola is

(a) $2 x - 5 \sqrt{y} - 20 = 0$

(b) $2 x - \sqrt{5} y + 4 = 0$

(d) $4 x - 3 y + 4 = 0$

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Answer:

Correct Answer: 14. (b)

Solution:

Equation of tangent to hyperbola having slope $m$ is

$y = m x + \sqrt{9 m^{2} - 4}$

Equation of tangent to circle is

$y = m (x - 4) + \sqrt{16 m^{2} + 16}$

Eqs. (i) and (ii) will be identical for $m = \frac{2}{\sqrt{5}}$ satisfy.

$∴$ Equation of common tangent is $2 x - \sqrt{5} y + 4 = 0$ .

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Hyperbola 2 Question 14

14.

Answer:

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