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

Question

kumar · Answer

circle passing through origin and center lying on the x-axis is x^2+y^2......M is mid point of the AB.

Ajay · Answer

Let (x 1 , y 1 ) be the middle point of chord of circle x 2 +y 2 =a 2 Then equation of chord can be written as xx 1 +yy 1 =x 1 2 +y 1 2 Since chord passes through (h,k) we have hx 1 +ky 1 =x 1 2 +y 1 2 Now replace x 1 by x and y 1 by y to get the locus of middle points as x 2 +y 2 = hx+ky

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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)

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