Find an equation for the ellipse described.
-Center at $( 0,0 )$; focus at $( - 5,0 )$; vertex at $( 8,0 )$

Question

Quizplus · Accepted Answer

The equation of an ellipse centered at the origin is $\frac{x^2}{a^2} + \frac{y^2}{b^2} = 1$, where $2a$ is the length of the major axis and $2b$ is the length of the minor axis. The distance from the center to a vertex (the semi-major axis, $a$), is 8, so $a^2 = 64$. The distance from the center to a focus (c) is 5, and $c^2 + b^2 = a^2$. Since $c = 5$, we have $25 + b^2 = 64$, giving $b^2 = 39$. Thus, the correct equation is $\frac{x^2}{64} + \frac{y^2}{39} = 1$, which is not exactly listed among the options. However, the closest match based on the context of the question and the values given for $a^2$ and the focus is option A, assuming a typographical error in the question or a misunderstanding in the calculation of $b^2$. The correct calculation for $b^2$ should directly follow from the given information, but none of the provided options accurately reflect the correct $b^2$ based on the standard formula. Given the options, A is chosen based on the correct value of $a^2 = 64$, but please note the discrepancy in the calculation of $b^2$.

Find an Equation for the Ellipse Described (0,0)( 0,0 )(0,0) ; Focus At

Find an Equation for the Ellipse Described $( 0,0 )$ ; Focus At