Question

What is equation of circle passing through two points and having its center on a given line?

Answer 1

First, find the center (a,b)(a,b). It is equidistant from the two points, soa2+(b−2)2−−−−−−−−−−√=(a−6)2+(b−6)2−−−−−−−−−−−−−−−√a2+(b−2)2=(a−6)2+(b−6)2ora2+(b−2)2=(a−6)2+(b−6)2.a2+(b−2)2=(a−6)2+(b−6)2.Now, since the center is on the line x−y=1x−y=1, we know that a−b=1a−b=1, ora=b+1.a=b+1.Substitute this into the quadratic equation above and simplify:(b+1)2+(b−2)2(b2+2b+1)+(b2−4b+4)2b2−2b+520bb=((b+1)−6)2+(b−6)2=(b2−10b+25)+(b2−12b+36)=2b2−22b+61=56=145.(b+1)2+(b−2)2=((b+1)−6)2+(b−6)2(b2+2b+1)+(b2−4b+4)=(b2−10b+25)+(b2−12b+36)2b2−2b+5=2b2−22b+6120b=56b=145.Therefore,a=145+1=195.a=145+1=195.What is the radius rr? Well the square of the radius isr2=a2+(b−2)2=(195)2+(45)2=37725.r2=a2+(b−2)2=(195)2+(45)2=37725.Putting this together, we can write the equation of the circle as(x−195)2+(y−145)2=37725(x−195)2+(y−145)2=37725or, by multiplying by 2525 to clear denominators,(5x−19)2+(5y−14)2=377.

Answer 2

http://taps.io/tpg2?r=NOAD121