Question

A circle touching the $x$ -axis at $\left(\right.3,0\left.\right)$ and making an intercept of length $8$ units on the $y$ -axis, passes through the point

• A. $\left(\right.3,10\left.\right)$
• B. $\left(\right.2,3\left.\right)$
• C. $\left(\right.1,5\left.\right)$
• D. $\left(\right.3,5\left.\right)$

Answer 1

Answer: (A)

Equation of circles are $\left\{\begin{array}{l}(x-3)^{2}+(y-5)^{2}=25 \\ (x-3)^{2}+(y+5)^{2}=25\end{array}\right.$

$\Rightarrow\left\{\begin{array}{l}x^{2}+y^{2}-6 x-10 y+9=0 \\ x^{2}+y^{2}-6 x+10 y+9=0\end{array}\right.$