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A circle touches the x-axis and also touches the circle with centre at (0, 3) and radius 2. The locus of the centre of the circle is ?

A circle touches the x-axis and also touches the circle with centre at (0, 3) and radius 2. The locus of the centre of the circle is ?

Grade:12

1 Answers

SHAIK AASIF AHAMED
askIITians Faculty 74 Points
9 years ago
Hello student,
Equation of circle with centre (0, 3) and radius 2 is
x2 + (y – 3)2= 4.
Let locus of the variable circle is (α, β)
∵It touches x-axis.
∴ It equation (x - α)2 + (y - β)2 = β2
Circles touch externally
∴ α2+ (β − 3)2= 2 + β
α2+ (β - 3)2= β2+ 4 + 4β
α2 = 10(β - 1/2)
∴ Locus is x2 = 10(y – 1/2) which is parabola.
Thanks and Regards
Shaik Aasif
askIITians faculty

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