- #1

Monoxdifly

MHB

- 284

- 0

A. \(\displaystyle x^2+y^2+6x-8y=0\)

B. \(\displaystyle x^2+y^2-6x-8y=0\)

C. \(\displaystyle x^2+y^2-8x-6y=0\)

D. \(\displaystyle x^2+y^2+8x+6y=0\)

E. \(\displaystyle x^2+y^2-4x-3y=0\)

Since the equation of a circle is \(\displaystyle x^2+y^2+Ax+By+C=0\), I substituted both known points to the equation and got C = 0 as well as B = -6, so the answer is obviously B. But then my student asked "What if all options have -6 as their B? How would we know the answer?". I think it has something to do with that \(\displaystyle y=\frac{4}{3}x\), but how? Please give me some hints.