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CGP EDU Academic Team
Published on: August 14, 2026
If a circle be drawn so as always to touch a given straight line and also a given circle externally then prove that the locus of its centre is a parabola.(given line and given circle are non intersecting)
Text Solution
Verified by ExpertsThe correct answer is:
CHECK THE SOLUTION.
Let the equation of circle and line are
x 2 + y 2 = a 2 and y = b
⇒ PQ – a = r
PQ = a + r
= (a + r) 2
h 2 + k 2 = (a + k – b) 2
h 2 + k 2 = k 2 + (a – b) 2 + 2k (a – b)
Locus x 2 = (a – b) 2 + 2y (a – b)
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