Answer  fast T h r o u g h   a   f i x e d   p o i n t   ( h , k ) , s e c a n t s   a r e   d r a w n   t o   t h e   c i r c l e   x 2 + y 2 = r 2 . S h o w   t h a t   t h e   l o c u s   o f   m i d   p o i n t   o f   t h e   t h e   p o r t i o n s   o f   s e c a n t s   i n t e r c e p t e d   b y   t h e   i r c l e   i s   x 2 + y 2 = h x + k y .
 

Dear Student,
Please find below the solution to the asked query:

x2+y2=r2We know that equation of chord having mid point x1,y1 is T=S1xx1+yy1-r2=x12+y12-r2xx1+yy1=x12+y12Now this chord passes through h,khx1+ky1=x12+y12Hence for locus replace x1x and y1yx2+y2=hx+ky

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