Question

Middle point of the chord of the circle $x^2+y^2=25$ intercepted on the line $x-2y=2$ is

• A. $(\frac{3}{5},\frac{4}{5})$
• B. $(-2,-2)$
• C. $(\frac{2}{5},-\frac{4}{5})$
• D. $(\frac{8}{3},\frac{1}{3})$

Answer 1

Answer: (C)

$(\frac{2}{5},-\frac{4}{5})$

Given, $x=2y+2,x^2+y^2=25$

for points of intersection $(2y+2{)}^2+y^2=25$

$4y^2+4+8y+y^2=25$

$5y^2+8y-21=0$

sum of roots $=y_1+y_2=\frac{-8}{5}----\left(1\right)$

Mid point of chord $=(\frac{x_1+x_2}{2},\frac{y_2+y_2}{2})=(y_1+y_2+2,\frac{y_1+y_2}{2})$

$=[(-\frac{8}{5}+2),(-\frac{-4}{5})]=\frac{2}{5},\frac{-4}{5}$

$\therefore$ Oprion $C$ is correct