question_answer

A circle touching the x-axis at (3, 0) and making an intercept of length 8 on the y-axis passes through the point : [JEE Main 12-4-2019 Afternoon]

A) (3, 10)

B) (2, 3)

C) (1, 5)               

D) (3, 5)

Correct Answer: A

Solution :

Equation of circles are \[\left\{ \begin{matrix}    {{\left( x-3 \right)}^{2}}+{{\left( y-5 \right)}^{2}}=25  \\    {{\left( x-3 \right)}^{2}}+{{\left( y+5 \right)}^{2}}=25  \\ \end{matrix} \right.\] \[\Rightarrow \left\{ \begin{matrix}    {{x}^{2}}+{{y}^{2}}-6x-10y+9=0  \\    {{x}^{2}}+{{y}^{2}}-6x+10y+9=0  \\ \end{matrix} \right.\]