Solving the quadratic equation \(\displaystyle{a}{X}^{{2}}+{a}{Y}^{{2}}+{2}{b}{X}+{2}{c}{Y}+{d}={0}\)

Sage Fry

Sage Fry

Answered question

2022-03-31

Solving the quadratic equation aX2+aY2+2bX+2cY+d=0

Answer & Explanation

Cody Hart

Cody Hart

Beginner2022-04-01Added 11 answers

Assuming b2+c2d,a0, you can always choose a>0 and then

(x+ba)2+(y+ca)2=r2x2+y2+2bax+2cay+b2+c2a2=r2ax2+ay2+2bx+2cy+(b2+c2ar2)d=0
is a real circle with center (ba,ca) and r=b2+c2da

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