Question
Question: The tangents drawn from the origin to the circle x<sup>2</sup>+y<sup>2</sup>-2rx-2hy+h<sup>2</sup> ...
The tangents drawn from the origin to the circle
x2+y2-2rx-2hy+h2 = 0 are perpendicular if
A
h = ± 2r
B
h = ± r
C
r2+h2 = 1
D
None
Answer
h = ± r
Explanation
Solution
The combined equation of the tangents drawn from (0,0) to x2+y2–2rx-2 hy + h2 = 0 is
(x2+y2 – 2 rx-2 hy + h2)h2 = (-rx – hy + h2)2.
This equation represents a pair of perpendicular straight lines if the coefficient of x2 + coefficient of y2 = 0
i.e. 2h2 – r2 – h2 = 0 ⇒ r2 = h2 or r = ± h