91Ó°ÊÓ

Write the standard form of the equation of a horizontal or vertical ellipse centered at \((h, k)\)

Find the \(x\) -and the \(y\) -intercepts of the graph of \(\frac{x^{2}}{a^{2}}+\frac{y^{2}}{b^{2}}=1\)

A. What is the standard form of the equation of a parabola opening upward or downward? B. What is the standard form of the equation of a parabola opening to the right or left?

Find the solutions of the system \(\left\\{\begin{array}{l}x^{2}+4 y^{2}=25 \\\ x^{2}-2 y^{2}=1\end{array}\right.\) on the right.

Find a substitution equation that can be used to solve the system: $$\left\\{\begin{array}{l}x^{2}+y^{2}=9 \\ 2 x-y=3\end{array}\right.$$

Determine whether the graph of each equation is a circle or a parabola. A. \(x^{2}+y^{2}-6 x+8 y-10=0\) B. \(y^{2}-2 x+3 y-9=0\) C. \(x^{2}+5 x-y=0\) D. \(x^{2}+12 x+y^{2}=0\)

Consider the system: \(\left\\{\begin{array}{l}6 x^{2}+y^{2}=9 \\ 3 x^{2}+4 y^{2}=36\end{array}\right.\) a. If the \(y^{2}\) -terms are to be eliminated, by what should the first equation be multiplied? b. If the \(x^{2}\) -terms are to be eliminated, by what should the second equation be multiplied?

Find two points on the graph of \(\frac{x^{2}}{16}+\frac{y^{2}}{4}=1\) by letting \(x=2\) and finding the corresponding values of \(y .\)

Suppose you begin to solve the system \(\left\\{\begin{array}{l}x^{2}+y^{2}=10 \\\ 4 x^{2}+y^{2}=13\end{array}\right.\) and find that \(x\) is \(\pm 1 .\) Use the first equation to find the corresponding \(y\) -values for \(x=1\) and \(x=-1 .\) State the solutions as ordered pairs.

Draw a parabola using the given facts. Opens right Passes through \((-2,1)\) Vertex \((-3,2)\) \(x\) -intercept \((1,0)\)