Find the equation of the circle on the straight line joining the points of intersection of `ax^2+2hx y+b y^2=0 and lx+my=1` as diameter.

Explanation

Let the equations of given curve and straight line are
`ax^2+2hxy+by^2=0 ` ......(1)
and lx+my=1 ....(2)

Let `A(x_1​,y_1​)` and `B(x_2​,y_2​)` be the points of intersection of (1) and (2)

From (2) we have my=1−lx
or `y=(1−lx)/m`​ .......(3)

Put the value of y in (3) in (1) we get

`ax^2+2hx(1−lx​)/m+b((1−lx​)/m)^2=0`

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