Question

The length of the common chord of the circle $x^2+y^2+4x+6y+4=0$ and $x^2+y^2+6x4y+4=0$ is-

• A. $\sqrt{10}$
• B. $\sqrt{22}$
• C. $\sqrt{34}$
• D. $\sqrt{38}$

Answer 1

The correct option is A $\sqrt{10}$

When two circles's radii are the same and their centres just have x and y coordinates interchanged there is a shorthand for length of common chord:

$\sqrt{\frac{1}{2}(g+f{)}^2-4c}$

$=\sqrt{\frac{1}{2}(4^2+6^2)-16}=\sqrt{10}$

This formula can easily be proved by Pythagoras' theorem.