Review Exercises

$y=x^2+4x-3$

$y=\mathrm{-6}{x}^2+12x-1$

$y=x^2+4x+7$

$y=\mathrm{-3}{x}^2-18x-29$

$x=2y^2$

$x=\text{−}{y}^2+2y-4$

$x=4y^2+8y$

$x=\text{−}{y}^2-6y-7$

$\frac{x^2}{36}+\frac{y^2}{25}=1$

$49x^2+64y^2=3136$

$\frac{{\left(x-1\right)}^2}{25}+\frac{{\left(y-6\right)}^2}{4}=1$

$\frac{{\left(x-5\right)}^2}{16}+\frac{{\left(y+3\right)}^2}{36}=1$

$4x^2+16y^2+48x+160y+480=0$

$25x^2+4y^2+150x+125=0$

A comet moves in an elliptical orbit around a sun. The closest the comet gets to the sun is approximately 10 AU and the furthest is approximately 90 AU. The sun is one of the foci of the elliptical orbit. Letting the ellipse center at the origin and labeling the axes in AU, the orbit will look like the figure below. Use the graph to write an equation for the elliptical orbit of the comet.

$\frac{y^2}{49}-\frac{x^2}{16}=1$

$16x^2-4y^2=64$

$\frac{{\left(x-2\right)}^2}{4}-\frac{{\left(y-3\right)}^2}{16}=1$

$\frac{{\left(y-1\right)}^2}{25}-\frac{{\left(x-2\right)}^2}{9}=1$

$16x^2-4y^2-64x-24y-36=0$

$36y^2-16x^2-96x+216y-396=0$

ⓐ $x^2+y^2+4x-10y+25=0$
ⓑ $y^2-x^2-4y+2x-6=0$
ⓒ $x=-y^2-2y+3$
ⓓ $16x^2+9y^2=144$

$\{\begin{array}{c}y=x^2-4\hfill \\ y=x-4\hfill \end{array}$

$\{\begin{array}{c}{x}^2+y^2=25\hfill \\ y=\mathrm{-5}\hfill \end{array}$

$\{\begin{array}{c}{x}^2+y^2=4\hfill \\ x-y=4\hfill \end{array}$

$\{\begin{array}{c}{x}^2+4y^2=4\hfill \\ 2x-y=1\hfill \end{array}$

$\{\begin{array}{c}{x}^2-y^2=5\hfill \\ -2x^2-3y^2=\mathrm{-30}\hfill \end{array}$

$\{\begin{array}{c}{x}^2+y^2=14\hfill \\ x^2-y^2=16\hfill \end{array}$

The difference of the squares of two numbers is 45. The difference of the square of the first number and twice the square of the second number is 9. Find the numbers.

Colton purchased a larger microwave for his kitchen. The diagonal of the front of the microwave measures 34 inches. The front also has an area of 480 square inches. What are the length and width of the microwave?