Tangent line
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Nice Idea
Find the tangent of  a circle x^2+y^2=25 on point (4,3)
Solution :
Prove that point (4,3) lies in a circle x^2+y^2=25
substitute (4,3) to a circle equation
4^2+3^2=16+9=25 right
thus this point should lie in that circle.
The tangent line to the circle at point (4,3) should be :
x1*x+y1*y=25 where (x1,y1)=(4,3) at a circle
4*x+3*y=25 is the tangent line you look for.