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find the locus of the middle points of chord of circle x^2+y^2=a^2 which pass through fixed point (h,k)

find the locus of the middle points of chord of circle x^2+y^2=a^2 which pass through fixed point (h,k)

Grade:12th pass

2 Answers

kumar
64 Points
5 years ago
circle passing through origin and center lying on the x-axis is x^2+y^2......M is mid point of the AB.
Ajay
209 Points
5 years ago
Let (x1, y1) be the middle point of chord of circle x2+y2=a2
Then equation of chord can be written as 
xx1+yy1=x12+y12
Since chord passes through (h,k) we have
hx1+ky1=x12+y12
Now replace x1 by x and y1 by y to get the locus of middle points as
x2+y2 = hx+ky

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