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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Mathtuition88 