CircleHardBloom L3
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:
Options
A.$x^{2} - 8y^{2} + 54x + 729 = 0$
B.$x^{2} - 8y^{2} - 54x + 729 = 0$
C.$x^{2} - 8y^{2} - 54x - 729 = 0$
D.$x^{2} - 8y^{2} = 729$
Solution
[Key Concept: $x = 3$ as a chord of contact of $x^{2} + y^{2} = 81$ fixes the pole; build the required circle from it.]
Equation of pair of tangents is
$$\begin{matrix} & \ (3x + 6\sqrt{2}y - 81)(3x - 6\sqrt{2}y - 81) = 0 \\ & \ (x - 27)^{2} - 8y^{2} = 0 \\ & x^{2} - 54x - 8y^{2} + 729 = 0 \end{matrix}$$
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