Chapter 4.4, Problem 5E

To determine

The correct match of the description of conic, “Ellipse with horizontal major axis” with the standard equations provided below:

$\begin{array}{l}\left(\text{a}\right)\frac{{\left(x-h\right)}^2}{a^2}+\frac{{\left(y-k\right)}^2}{b^2}=1,\left(\text{b}\right)\frac{{\left(x-h\right)}^2}{a^2}-\frac{{\left(y-k\right)}^2}{b^2}=1,\left(\text{c}\right)\frac{{\left(y-k\right)}^2}{a^2}-\frac{{\left(x-h\right)}^2}{b^2}=1\\ \left(\text{d}\right)\frac{{\left(x-h\right)}^2}{b^2}+\frac{{\left(y-k\right)}^2}{a^2}=1,\left(\text{e}\right){\left(x-h\right)}^2=4p\left(y-k\right),\left(\text{f}\right){\left(y-k\right)}^2=4p\left(x-h\right)\end{array}$