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 =  -1.334
y1 =  0.286
x2 =  -7.914
y2 =  5.926

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 1.73469387755x2+16.041x+18.306=0  a=1.73469387755;b=16.041;c=18.306 D=b2−4ac=16.0412−4⋅1.73469387755⋅18.306=130.285714286 D>0  x1,2=−b±D2a=−16.04±130.293.4693877551 x1,2=−4.62352941±3.28999742325 x1=−1.33353198852=−1.334 x2=−7.91352683501   Factored form of the equation:  1.73469387755(x+1.33353198852)(x+7.91352683501)=0

Checkout calculation with our calculator of quadratic equations.

y1=−6/7⋅ (x1+1)=−6/7⋅ ((−1.3335)+1)=5011750=0.286
y2=−6/7⋅ (x2+1)=−6/7⋅ ((−7.9135)+1)=5.926

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