A circle touches the `x`-axis and also touches the circle with center `(0, 3)` and radius `2`. The locus of the centerA. parabolaB. a hyperbolaC. a circleD. an ellipse

A circle touches the `x`-axis and also touches the circle with center

1.	A circle touches the `x`-axis and also touches the circle with center `(0, 3)` and radius `2`. The locus of the centerA. parabolaB. a hyperbolaC. a circleD. an ellipse
Answer» Correct Answer - A Let (h, k) be the coordinates of the centre of the circle. Since it touches x-axis. So, radius of the circle is \|k\|. This circle also touches a circle of radius 2 having centre at (0, 3). Therefore, distance between their centre is equal to sum or difference of their radii. i.e. `sqrt((h-0)^(2)+(k-3)^(2))=\|k\|pm2` `rArr h^(2)+(k-3)^(2)=k^(2)+4 pm 4k` `rArr h^(2)-10k+5=0 or, h^(2)-2k+5=0` Hence, the locus of (h, k) is `x^(2)-10y+5=0 or x^(2)-2y+5=0` which are equations of a parabola.

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