Question

What is the slope of a chord centered at (3, 2) in the circle $x^2+y^2=25$

• A. -1/2
• B. 1/2
• C. -3/2
• D. 3/2

Answer 1

The correct option is C

-3/2

Here the key point is that any chord of a circle is perpendicular to the radius passing through its midpoint P as shown in the figure

i.e., if M is midpoint of AB then $\angle APO={90}^{\circ }$
In the given question, slope of radius through $P=\frac{(2-0)}{(3-0)}=\left(\frac{2}{3}\right)$

$\therefore$ Slope of chord AB = $\left(\frac{-3}{2}\right)$