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) $2 x-\sqrt{5} y+4=0$
(c) $3 x-4 y+8=0$
(d) $4 x-3 y+4=0$
Integer Answer Type Question
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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.
$\therefore$ Equation of common tangent is $2 x-\sqrt{5} y+4=0$.
