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From the point P(3, 4) tangents are drawn to the ellipse x²/9 + y²/4 = 1, touching it at A and B. Find the equation of the locus of a point that is equidistant from P and from the line AB (the chord of contact).

1. 9x² + y² - 6xy - 54x - 62y + 241 = 0
2. x² + 9y² + 6xy - 54x + 62y - 241 = 0
3. 9x² + 9y² - 6xy - 54x - 62y - 241 = 0
4. x² + y² - 2xy + 27x + 31y - 120 = 0

Correct answer: 9x² + y² - 6xy - 54x - 62y + 241 = 0

Solution

AB is x + 3y = 3; equating the squared distances of a point from P(3,4) and from this line gives 9x² + y² - 6xy - 54x - 62y + 241 = 0.

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