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From P(2,3), tangents are drawn to the circle x² + y² - 8x + 6y + 1 = 0, touching it at A and B. The circumcircle of triangle PAB cuts the director circle of the ellipse (x+5)²/9 + (y-3)²/b² = 1 orthogonally. Find b².
- 44
- 24
- 64
- 54
Correct answer: 54
Solution
Setting up the orthogonality condition between the circumcircle (diameter PC) and the director circle (centre (-5,3), radius² = 9 + b²) yields b² = 54.
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