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A circle touches the `x`-axis and also touches the circle with center `(0, 3)` and radius `2`. The locus of the centerA. a circleB. an ellipseC. a parabolaD. a hyperbola |
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Answer» Correct Answer - C (3) Let `C_(1)(h,k)` be the centre of the circle. The circle touches the c-axis. Then its radius is `r_(1)=k` Also, the circle touches the circle with center `C_(2)(0,3)` and radius `r_(2)=2`. Therefore, `|C_(1)C_(2)|=r_(1)+r_(2)` `orsqrt((h-0)^(2)+(k-3)^(2))=|k+2|` Squaring, we get `h^(2)-10k+5=0` Therefore, the locus is `x^(2)-10y+5=0`, which is a parabola. |
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