Questions
A circle touches the axis and also touches the circle with centre at and radius . The locus of the centre of the circle is
a
a hyperbola
b
a parabola
c
an ellipse
d
a circle
detailed solution
Correct option is B
Let (h, k) be the centre of the circle. Since it touches x-axis, its radius is k. As it also touches the circle with centre (0, 3) and radius 2 (externally as x-axis lies outside the given circle) distance between the centres is equals to the sum of their radii.So h2+(k−3)2=(k+2)2⇒ h2=5(2k−1)Locus of the centre (h, k) is x2=5(2y−1)which is a parabola.Talk to our academic expert!
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