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

Answer: (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, $x_1-x_2=\sqrt{{\left(x_1+x_2\right)}^2-4x_1{x}_2}$
$=\sqrt{{\left(16\right)}^2+\left(4\times 36\right)}=\sqrt{400}=20=$ Intercept on $x$-axis