Find \(x\) so that \((x,2)\) is \(2\sqrt{5}\) units for \((-1,4)\).

Give the equation of the circle with center at \((-2,4)\) and radius \(3\).

Give the equation of the circle with center at the origin that contains the point \((-3,-4)\).

Find the center and radius of the circle: \(x^2+y^2-10x+6y=5\)

Graph each of the following: \(4x^2-y^2=16\)

Graph each of the following:
\(\displaystyle\frac{x^2}{25}+\displaystyle\frac{y^2}{4}=1\)

Graph each of the following:
\((x+2)^2+(y+1)^2\leq 9\)

Graph each of the following:
\(9x^2+4y^2-72x-16y+124=0\)

Solve the following system:

\[\begin{aligned} x^2+y^2 &= 25\\ 2x+y &= 5\end{aligned}\]

Solve the following system:

\[\begin{aligned} x^2+y^2 &= 16\\ y&=x^2-4\end{aligned}\]

Mini Lecture

1. Find the distance between \((3,-5)\) and \((-2,1)\).

2. Find \(x\) so the distance between \((x,2)\) and \((1,5)\) is \(\sqrt{13}\).

3. Find the equation of the circle with its center at \((3,-2)\) and radius \(3\).

Graph the following

Mini Lecture
Graph:

1. \(y=-x^2-2x+3\)

2. \(y=-2x^2+6x-5\)

Mini Lecture
Graph the following ellipses.

1. \(\displaystyle\frac{x^2}{16}+\displaystyle\frac{y^2}{9}=1\)

2. \(x^2+8y^2=16\)

Graph the following hyperbolas.

3. \(\displaystyle\frac{x^2}{16}-\displaystyle\frac{y^2}{9}=1\)

4. \(x^2-4y^2=4\)

Mini Lecture
Graph the following ellipses.

1. \(\displaystyle\frac{x^2}{16}+\displaystyle\frac{y^2}{9}=1\)

2. \(x^2+8y^2=16\)

Graph the following hyperbolas.

3. \(\displaystyle\frac{x^2}{16}-\displaystyle\frac{y^2}{9}=1\)

4. \(x^2-4y^2=4\)

Graph \(x^2+y^2<16\)

Graph \(y\leq x^2-2\)

Graph \(4y^2-9x^2<36\)

Graph the solution set for the system

\[\begin{aligned} x^2+y^2 &\leq 9\\ \frac{x^2}{4}+\frac{y^2}{25} &\geq 1\end{aligned}\]

Mini Lecture
Graph the following.

1. \((x-2)^2+(y+3)^2<16\)

2. \[\begin{aligned} x^2+y^2&<9\\ y&\geq x^2-1\end{aligned}\]

3. Solve the system

   \[\begin{aligned} x^2+y^2&=9\\ 2x+y&=3\end{aligned}\]