The equation to the chord of the circle x2+y2=9 whose middle point is (1,−2) is
We have,
Given equation of circle is x2+y2=9
On comparing that,
x2+y2=a2
Now,
Centre is (x1,y1)=(0,0)
(x2,y2)=?
And equation of chord is =?
So,
Middle point (x1,y1)=(1,−2)
So,
Using middle point formula,
x=x1+x22,y=y$1+y22
⇒1=0+x22,−2=0+y22
⇒(x2,y2)=(2,−4)
Now,
Equation of chord is
y−y1=y2−y1x2−x1(x−x1)
⇒y+2=−4+22−1(x−1)
⇒y+2=−2(x−1)
⇒y+2=−2x+2
⇒y=−2x
⇒2x+y=0
Hence, this is the
answer.