Question

Equation of chord of the circle $x^2 + y^2 + 4x - 6y - 9 = 0 $ bisected at (0, 1) is

• A. $ y - 1 = x$
• B. $ y + 1 = x$
• C. $ y + 1 = 2x$
• D. $ y - 1 = 3x$

Answer 1

The Correct Option is A

Since chord of circle
$x^2 + y^2 +4x - 6y- 9 = 0$ bisected at (0, 1)
$\Rightarrow \:\:\: OC \bot AB$
$ \therefore$ Slope of $OC \times $ Slope of $AB= -1$
Centre of given circle is (-2, 3) and mid-point of chord is $(0,1)$
Let any other point of chord is $ (x, y)$ then slope of chord is $\frac{y-1}{x-0} $ and slope of $ OC = \frac{3-1}{-2-0} $
$\therefore \:\:\: \left(\frac{3-1}{-2-0}\right) \left(\frac{y-1}{x-0}\right) = - 1 $
or $\left(\frac{2}{-2}\right) \left( \frac{y-1}{x}\right) = -1$
or $\frac{y-1}{x} = 1$ or $y - 1 =x$
is the required equation of chord.