Graph the equation. Begin by completing the square on the first two terms.

Question

Quizplus · Accepted Answer

The given equation is: 
$$3x^2 + 6x + 5y^2 - 10y - 17 = 0$$
Completing the square on the first two terms:
$$3(x^2 + 2x) + 5y^2 - 10y - 17 = 0$$
Adding and subtracting $(2/3)^2$ inside the bracket to complete the square for $x$:
$$3(x^2 + 2x + 1 - 1) + 5y^2 - 10y - 17 = 0$$
Simplifying:
$$3(x+1)^2 + 5(y-1)^2 = 35$$
Dividing throughout by $35$:
$$\frac{(x+1)^2}{35/3} + \frac{(y-1)^2}{7} = 1$$
Thus, the equation represents an ellipse centered at $(-1,1)$ with semi-major and semi-minor axes lengths $\sqrt{35/3}$ and $\sqrt{7}$, respectively. The correct choice is option (B).

Graph the Equation