Equation of mid point chord:

Equation of mid chord the  midpoint of which is (x₁,y₁)  is given by

T=S₁          here 

Illustration: Find locus of midpoint of chords of the ellipse  , which are parallel to the line y = 2x + c.

Solution:   Let the midpoint of chord be (h, k). Then equation of this chord will be

                             T = S₁

                              Slope of the line 

                              Required locus is 

Illustration:  Find locus of the middle point of chord of ellipse which are drawn through positive end of the minor axis.

Solution:               Let the middle point be (h, k), so equation is T = S₁

                              => . As it passes through point (0, b)

            so, 

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