question_answer

The equation of two circles which touch the Y-axis at \[(0,3)\] and make an intercept of 8 unit on X-axis are

A)  \[{{x}^{2}}+{{y}^{2}}\pm 10x-6y+9=0\]

B)  \[{{x}^{2}}+{{y}^{2}}\pm 6x-10y+9=0\]

C)  \[{{x}^{2}}+{{y}^{2}}-8x\pm 10y+9=0\]

D)  \[{{x}^{2}}+{{y}^{2}}+10x\pm 6y+9=0\]

Correct Answer: A

Solution :

Given, equation of circle touch the  y-axis at \[(0,3)\]. So, from figure                                 \[r=\sqrt{{{3}^{2}}+{{4}^{2}}}=5\] The point \[(0,3)\] and radius 5 satisfies the equation \[{{x}^{2}}+{{y}^{2}}\pm 10x-6y+9=0.\] Hence, it is the required equation of circle;