question_answer

The circle passing through \[(1,-2)\] and touching the x-axis at \[(3,0)\] also passes through the point

A) \[(-5,2)\]                             

B) \[(2,-5)\]

C) \[(5,-2)\]                             

D) \[(-2,5)\]

Correct Answer: C

Solution :

\[\therefore \]Equation of required circle                 is \[{{(x-3)}^{2}}+{{y}^{2}}+\lambda y=0\]                 as, \[(1,\,\,-2)\] satisfy it, so \[\Rightarrow \,2(\sin \theta \,+\cos \theta )\,.(\sin \theta -\cos \theta )=0\] \[\therefore \]The equation of circle is \[{{x}^{2}}+{{y}^{2}}-6x+4y+9=0\] Clearly,\[(5,\,\,-~2)\] satisfy it.