Generalized Analytic Geometry

Find the equation of the circle which cuts the tangent 2x-y=0 at M(1,4), passing thru point A(4,-1).

**Solution**:

**1st generalization**:

Let the point circle be:

(x-1)² + (y-4)² =0

**2nd generalization**:

It cuts the tangent 2x-y=0

(x-1)² + (y-4)² +**k**(2x-y) =0 …(C)

Pass thru A(4,-1)

x=4, y= -1

=> k= -2

(C): (x-3)² + (y-1)² =…

[QED]

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