State whether the graph of each equation is a circle, a line or a parabola

Question

1. x^2+y^2= 25
2. (x^2-4)+(y^2+2)=225
3. x^2+y=225
4. x+y=55

Answer 1

You can graph these if you want, some are a bit large so you want to check with a calculator or at Desmos.com

X² + Y² = 25 is a circle centered at (0,0) with a radius of 5

(x² -4) + (y² + 2) = 225 is a circle with a radius of 15 for this substituting (0,0) in for (h,k) gives

x² + y² = 225

x² + y = 225 is

y =225 - x² A Parabola opens downward from 225 along the y- axis

You can set this quadratic equal to 0 and factor it to get the x intercepts

0 = 225 - x²

0 = (15 -x)(15 + x)

x + y = 55 is the line

y = -x + 55 with (0, 55) as the y intercept and (55, 0) as the x intercept