Write this in standard form

Question

X + y^2 = 0 write it in standard form

and

13x^2 - y^2 + 2y + 12 = 0

Answer 1

x = -y^2 this parabola opens to the left

The second equation is an ellipse:

x^2 - (1/13) y^2 + (2/13) y = -12/13

x^2 - (1/13) [ y^2 + 2 y ] =12/13

x^2 - (1/13) [ y^2 + 2y + 1] = 12/13 -1/13 <--- completes the square

x^2 - (1/13] (y +1)^2 = 11/13

x^2 - (y+1)^2/13 = 11/13

the ellipse has center at (0, -1)

the horizontal radius is 1

the vertical radius is sqrt(1/13) = sqrt(13)/13