A) A circle
B) An ellipse
C) A parabola
D) A hyperbola
Correct Answer: C
Solution :
[c] Let \[{{C}_{1}}(h,k)\]be the center of the circle. The circle touches the x-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, \[\left| {{C}_{1}}{{C}_{2}} \right|={{r}_{1}}+{{r}_{2}}\] Or \[\sqrt{{{(h-0)}^{2}}+{{(k-3)}^{2}}}=\left| k+2 \right|\] Squaring. We get \[{{h}^{2}}-10k+5=0\] Therefore, the locus is \[{{x}^{2}}-10y+5=0\], which is a parabola,
You need to login to perform this action.
You will be redirected in
3 sec
