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Consider the conic C: x²/16 + y²/12 = 1. A circle touches C at one extremity of a latus rectum and passes through the centre of C. The equation of such a circle is:
- 8x² + 8y² - 19x - 22y = 0
- 8x² + 8y² - 19x + 22y = 0
- 8x² + 8y² + 19x - 22y = 0
- 8x² + 8y² + 19x + 22y = 0
Correct answer: 8x² + 8y² - 19x - 22y = 0
Solution
Taking the extremity (2, 3), the circle through the origin tangent to the ellipse there is 8x² + 8y² - 19x - 22y = 0 (other extremities give the other listed options).
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