Question

If $x=3$ is the chord of contact of the circle $x^{2}+y^{2}=81$ , then the equation of the corresponding pair of tangents, is

• A. $\text{x}^{2} - 8 \text{y}^{2} + 5 4 \text{x} + 7 2 9 = 0$
• B. $\text{x}^{2} - 8 \text{y}^{2} - 5 4 \text{x} + 7 2 9 = 0$
• C. $\text{x}^{2} - 8 \text{y}^{2} - 5 4 \text{x} - 7 2 9 = 0$
• D. $\text{x}^{2} - 8 \text{y}^{2} = 7 2 9$

Answer 1

Answer: (B)

Put $\text{x} = 3$ in the equation of circle to get the point of contact, $\text{y} = \pm 6 \sqrt{2}$
Hence, equation of the pair of tangents is
$\left(3 \text{x} + 6 \sqrt{2} y - 8 1\right) \left(3 \text{x} - 6 \sqrt{2} \text{y} - 8 1\right) = 0$
$\left(\text{x} - 2 7\right)^{2} - 8 \left(\text{y}\right)^{2} = 0$
$\text{x}^{2} - 5 4 \text{x} - 8 \text{y}^{2} + 7 2 9 = 0$