Question

If the line $x+2by+7=0$ is a diameter of the circle $x^2+y^2-66x+2y=0$, then $b=$

• A. $30$
• B. $-50$
• C. $-1$
• D. $20$

Answer 1

Answer: (D)

$20$

Solution:-

Equation of circle-

$x^2+y^2-66x+2y=0$

$\Rightarrow {(x-33)}^2+{(y+1)}^2-1-1089=0$

$\Rightarrow {(x-33)}^2+{(y+1)}^2=1090$

Centre of circle $\equiv (33,-1)$

Given that the line $x+2by+7=0$ is the diameter of circle.

Hence the line passes through the centre of circle $(33,-1)$.

$\therefore 33+2b(-1)+7=0$

$\Rightarrow 40-2b=0$

$\Rightarrow b=20$

Hence the value of $b$ is $20$.