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A variable circle is drawn so that it touches the line 3x - 4y = 10 and also touches the fixed circle x² + y² = 1 externally. Find the locus of the centre of the variable circle.
- parabola
- straight line
- circle
- pair of real, distinct straight lines
Correct answer: parabola
Solution
Eliminating r gives distance(P, O) = distance(P, line) + 1, i.e. distance from P to a fixed point equals distance from P to a fixed line (after shifting the line), which defines a parabola.
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