Question

The equation of a circle is $x^2+y^2=25$, The equation of its chord whose middle point is $(1,-2)$ is given by:

• A. $x+2y+5=0$
• B. $2x-y+5=0$
• C. $x-2y-5=0$
• D. $2x+y+5=0$

Answer 1

The correct option is C $x-2y-5=0$

The line from the center of the circle to the midpoint of a chord is perpendicular to the chord.

The center of the circle $x^2+y^2=25$ is $(0,0)$.

And the slope of the line joining $(0,0)$ to $(1,-2)$ is $\frac{-2-0}{1-0}=-2$

So the slope of the chord with midpoint $(1,-2)$ is $\frac{-1}{-2}=\frac{1}{2}$.

Thus the equation of the chord is $y+2=\frac{1}{2}(x-1)\Rightarrow x-2y-5=0$

So option C is the right answer.