Find the centre and radius of the circle x^2 + y^2 - 6y +4y + 8 =0 .Also find the equation of the tangent to this circle at (1, -3)
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x^2 + y^2 - 6x +4y + 8 =0
2g = -6 and 2f = 4
g = -3 and f = 2
Centre = (-g,-f) = (3,-2)
Equation of tangent is xx1+yy1+g(x+x1)+f(y+y1)+c= 0
(x1,y1) = (1,-3)
x-3y -3(x+1) +2(y-3) + 8 = 0
x- 3y-3x-3+2y - 6+8 = 0
-2x-y-1 = 0
2x+y+1 = 0 is the tangent
2g = -6 and 2f = 4
g = -3 and f = 2
Centre = (-g,-f) = (3,-2)
Equation of tangent is xx1+yy1+g(x+x1)+f(y+y1)+c= 0
(x1,y1) = (1,-3)
x-3y -3(x+1) +2(y-3) + 8 = 0
x- 3y-3x-3+2y - 6+8 = 0
-2x-y-1 = 0
2x+y+1 = 0 is the tangent
satyajit9:
can you prove the equation of tangent xx1 +yy1 +g(x+x1)+f(y+y1)+c=0
post it as a separate question for the proof
If not me, someone will answer
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