Question

Question: Consider the equation x2 + y2 – 10x + 6y = 15. A. Complete both squares in the equation. Show your work. B. Which conic section is this an equation of? How do you know?

Answer 1

Part A:


`x^(2) + y^(2) -10x+6y=15 \\ \\ x^(2) -2(x)(5)+ y^(2)+2(y)(3)=15 \\ \\ x^(2) -2(x)(5)+(5)^(2)+ y^(2)+2(y)(3)+(3)^(2)=15+ (5)^(2)+(3)^(2) \\ \\ (x-5)^(2)+(y+3)^(2)=49`

Part B:
Since the signs and the coefficient of squared terms are the same in the given equation, the given equation represents a circle. The center of the circle is (5, -3) and the radius of the circle is 7.