SOLUTION: Given the circle x^2+y^2-4x+y=7 1 determine the equation of the tangent to the circle at the point where x=-1 2 determine the point of intersection of these two tangents

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Question 1088892: Given the circle x^2+y^2-4x+y=7
1 determine the equation of the tangent to the circle at the point where x=-1
2 determine the point of intersection of these two tangents
Answer by josgarithmetic(39616) About Me  (Show Source):
You can put this solution on YOUR website!
y%5E2%2By=-x%5E2%2B4x%2B7
y%5E2%2By-4x-%2Bx%5E2-7=0
y%5E2%2By%2B4%2B1-7=0
y%5E2%2By-2=0
y=%28-1%2B-+sqrt%281%2B4%2A2%29%29%2F2
y=%28-1%2B-+3%29%2F2
system%28y=-2%2Cor%2Cy=1%29
The two lines are tangent at (-1,-2) and (-1,1).

x%5E2-4x%2By%5E2%2By=7
x%5E2-4x%2B4%2By%5E2%2By%2B%281%2F2%29%5E2=7%2B4%2B1%2F4
%28x-2%29%5E2%2B%28y%2B1%2F2%29%5E2=11%261%2F4
Center of the circle, (2, -1/2).

One line will have slope, the negative reciprocal of points (2, -1/2) and (-1,-2) and will contain (-1,-2); and the other line will have slope, the negative reciprocal of points (2, -1/2) and (-1,1) and will contain point (-1,1).
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Find equation of each of these lines, and find their intersection.