Identify the conic by writing the equation in standard form.
A) ; ellipse
B) ; ellipse
C) ; ellipse
D) ; ellipse
E) ; circle

Question

Identify the conic by writing the equation in standard form. 
A) ; ellipse 
B) ; ellipse 
C) ; ellipse 
D) ; ellipse 
E) ; circle

Quizplus · Accepted Answer

The standard form equation for an ellipse is:

$\frac{(x-h)^2}{a^2} + \frac{(y-k)^2}{b^2} = 1$

where (h,k) is the center of the ellipse and a and b are the lengths of the semi-major and semi-minor axes, respectively.

The given equation can be rewritten as:

$-2x^2 + 2y^2 + 880 = 0$

Dividing both sides by 880, we get:

$\frac{-2x^2 + 2y^2}{880} = -1$

Multiplying both sides by -1, we get:

$\frac{2x^2 - 2y^2}{880} = 1$

This is in the standard form equation of an ellipse with center at the origin, semi-major axis of $\sqrt{220}$ and semi-minor axis of $\sqrt{110}$. Thus, the conic is an ellipse and the best choice is (D).

Identify the Conic by Writing the Equation in Standard Form