Question 1088892
{{{y^2+y=-x^2+4x+7}}}

{{{y^2+y-4x-+x^2-7=0}}}

{{{y^2+y+4+1-7=0}}}

{{{y^2+y-2=0}}}

{{{y=(-1+- sqrt(1+4*2))/2}}}

{{{y=(-1+- 3)/2}}}

{{{system(y=-2,or,y=1)}}}
The two lines are tangent at (-1,-2) and (-1,1).


{{{x^2-4x+y^2+y=7}}}
{{{x^2-4x+4+y^2+y+(1/2)^2=7+4+1/4}}}
{{{(x-2)^2+(y+1/2)^2=11&1/4}}}
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.