Question

The equation of an ellipse is 4x'+y°+10y+13=0.
Write the equation in standard form.
(1 point)
+(2+5)2=1
4
3
+(8+5)} =1
4
+(8+5)3=1
3
+(2+5)3=1

Answer 1

Start with 4x^2 + y^2 + 10y + 13 = 0.
Complete the square in y: y^2 + 10y = (y+5)^2 − 25.
So 4x^2 + (y+5)^2 − 25 + 13 = 0 ⇒ 4x^2 + (y+5)^2 = 12.
Divide by 12: x^2/3 + (y+5)^2/12 = 1.

Thus the standard form is x^2/3 + (y+5)^2/12 = 1.
Center: (0, −5). Semi-axes: a = 2√3 (vertical), b = √3 (horizontal).