Intersections 3

Find the intersections of the circles
x2 + y2 + 6 x - 10 y + 9 = 0 and
x2 + y2 + 18 x + 4 y + 21 = 0

Correct result:

x1 =  -1.3335
y1 =  0.2859
x2 =  -7.9135
y2 =  5.9259

Solution:

x2+y2+6 x−10 y+9=0 x2+y2+18 x+4 y+21=0  e2−e1: (18−6)x+(4+10)y+(21−9)=0 y=−6/7(x+1)   x2+(−6/7(x+1))2+6x−10(−6/7(x+1))+9=0  x2+(−6/7(x+1))2+6 x−10(−6/7(x+1))+9=0 1.734693877551x2+16.041x+18.306=0  a=1.734693877551;b=16.041;c=18.306 D=b2−4ac=16.0412−4⋅1.734693877551⋅18.306=130.2857142857 D>0  x1,2=−b±D2a=−16.04±130.293.469387755102 x1,2=−4.62352941±3.2899974232486 x1=−1.3335319885161=−1.3335 x2=−7.9135268350134   Factored form of the equation:  1.734693877551(x+1.3335319885161)(x+7.9135268350134)=0

Our quadratic equation calculator calculates it.

y1=−6/7⋅ (x1+1)=−6/7⋅ ((−1.3335)+1)=0.2859
y2=−6/7⋅ (x2+1)=−6/7⋅ ((−7.9135)+1)=5.9259

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