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. ${\text{x}}^2-8{\text{y}}^2+54\text{x}+729=0$
• B. ${\text{x}}^2-8{\text{y}}^2-54\text{x}+729=0$
• C. ${\text{x}}^2-8{\text{y}}^2-54\text{x}-729=0$
• D. ${\text{x}}^2-8{\text{y}}^2=729$

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
$\left(3\text{x}+6\sqrt{2}y-81\right)\left(3\text{x}-6\sqrt{2}\text{y}-81\right)=0$
${\left(\text{x}-27\right)}^2-8{\left(\text{y}\right)}^2=0$
${\text{x}}^2-54\text{x}-8{\text{y}}^2+729=0$