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

• Correct answer
  A

  $x^{2}+y^{2} \pm 10 x-6 y+9=0$
• B

  $x^{2}+y^{2} \pm 6 x-10 y+9=0$
• C

  $x^{2}+y^{2}-8 x \pm 10 y+9=0$
• D

  $x^{2}+y^{2}+10 x \pm 6 y+9=0$

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 $x^{2}+y^{2} \pm 10 x-6 y+9=0$ Hence, it is the required equation of circle.

Hence, the correct answer is option: 'A'.