Question

The measure of the chord intercepted by circle $x^2+y^2=9$ and the line $x-y+2=0$ is.

• A. $\sqrt{28}$
• B. $2\sqrt{5}$
• C. $7$
• D. $5$

Answer 1

Answer: (A)

$\sqrt{28}$

Find $x_1,x_2,y_1,y_2$
Using both the equations we get,
$x_1=-\frac{2+\sqrt{14}}{2};y_1=\frac{2+\sqrt{14}}{2}$
$x_2=-\frac{2-\sqrt{14}}{2};y_2=\frac{2-\sqrt{14}}{2}$
Distance between these 2 points $P_1\&P_2$ = Length of chord
$\Rightarrow d=\sqrt{(x_2-x_1)+(y_2-y_1)}$
$d=\sqrt{{-(\frac{2+\sqrt{14}}{2}+\left(\frac{2-\sqrt{14}}{2}\right))}^2+{(\frac{2-\sqrt{14}}{2}+\frac{(2+\sqrt{14})}{2})}^2}$
$d=\sqrt{{(0+\sqrt{14})}^2+{(0-\sqrt{14})}^2}$
$d=\sqrt{14+14}$
$d=\sqrt{28}$, Length of chord