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From any point on the circle 15x² + 15y² - 48x + 64y = 0, tangents are drawn to the circles 5x² + 5y² - 24x + 32y + 75 = 0 and 5x² + 5y² - 48x + 64y + 300 = 0. The lengths of these tangents are in the ratio
- 1: 2
- 2: 3
- 3: 4
- None of these
Correct answer: 1: 2
Solution
Reduce all circles to monic form. For a point on the given circle, substitute S = x^2+y^2 from its equation into the tangent-length formulas: L1^2 = -(8/5)x+(32/15)y+15 and L2^2 = -(32/5)x+(128/15)y+60 = 4*L1^2. Hence L1:L2 = 1:2.
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