Question

The equation to the chord of the circle $x^2+y^2=9$ whose middle point is $(1,-2)$ is

• A. $x+2y+3=0$
• B. $2x+y=0$
• C. $x-2y-5=0$
• D. $3x+y-1=0$

Answer 1

Answer: (B)

$2x+y=0$

We have,

Given equation of circle is $x^2+y^2=9$

On comparing that,

$x^2+y^2=a^2$

Now,

Centre is $(x_1,y_1)=(0,0)$

$(x_2,y_2)=?$

And equation of chord is $=?$

So,

Middle point $(x_1,y_1)=(1,-2)$

So,

Using middle point formula,

$x=\frac{x_1+x_2}{2},y=\frac{y{\$}_1+y_2}{2}$

$\Rightarrow 1=\frac{0+x_2}{2},-2=\frac{0+y_2}{2}$

$\Rightarrow (x_2,y_2)=(2,-4)$

Now,

Equation of chord is

$y-y_1=\frac{y_2-y_1}{x_2-x_1}(x-x_1)$

$\Rightarrow y+2=\frac{-4+2}{2-1}(x-1)$

$\Rightarrow y+2=-2(x-1)$

$\Rightarrow y+2=-2x+2$

$\Rightarrow y=-2x$

$\Rightarrow 2x+y=0$

Hence, this is the answer.