Question

If the line x + $2by+7=0$ is a diameter of the circle x${}^2$ + y${}^2$ - $6y$ + $2y=0$, then b =

• A. $3$
• B. $-5$
• C. $-7/4$
• D. $5$

Answer 1

The correct option is C $-7/4$

$x^2+y^2-6y+2y=0$

$x^2+y^2-4y=0$

$C=(-g,-f)=(0,2)$

These points also pass through the equation of diameter,

$x+2by+7=0$

substituting the center points, we get,

$0+2b\left(2\right)+7=0$

$4b=-7$

$\therefore b=\frac{-7}{4}$