Question

Length of intercept made by the circle $x^{2} + y^{2} - 16x + 4y - 36 = 0$ on $x$-axis is

• A. $20$
• B. $10$
• C. $5$
• D. None of these

Answer 1

The Correct Option is A

As the circle meet $x$-axis at two points so put $y= 0$ in the equation of circle, we get $x^{2 }- 16x - 36 = 0$ Let two roots of the equation be $x_{1}$ and $x_{2}$. $ \Rightarrow\, x_{1}+x_{2}=16$ and $x_{1}x_{2}=-36$ Now, $ x_{1}-x_{2}=\sqrt{\left(x_{1}+x_{2}\right)^{2}-4x_{1}x_{2}}$ $=\sqrt{\left(16\right)^{2}+\left(4\times36\right)}=\sqrt{400}=20 =$ Intercept on $x$-axis