Question

A circle touches the axes at the point (3,0)and (0,-3). The centre of the circle is
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Answer 1

Answer:

Parabola

Step-by-step explanation:

Let C  1  (h,k) be the center of the circle.

Circle touches the x-axis then its radius is r   1   =k.

Also circle touches the circle with centre C   2  (0,3) and radius r   2  =2.

∴∣C   1  C   2   ∣=r   1   +r   2

$\sqrt{(h-0)^{2}+(k-3)^{2}$ = ( k+2)

Squaring

$h^{2}-10k+5=0$

⇒ Locus is  $x^{2} -10y+5$ , which is parabola.