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

Find \(x\) if the distance from \((x,5)\) to \((3,4)\) is \(\sqrt{2}\).

Find the equation of the circle with center at \((-3,2)\) having a radius of \(5\).

Give the equation of the circle with radius \(3\) whose center is at the origin.

If \((x-1)^2 +(y+3)^2=4\) find the center, radius, and graph the circle.

Sketch \(x^2+y^2=9\)

Sketch \(x^2+y^2+6x-4y-12=0\)

Graph \(y=2(x-1)^2-3\)

Graph \(y=x^2+4x+7\)

Graph \(y=-2x^2+8x+3\)

Graph \(x=-2(y+3)^2+4\)

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

Graph \(x=3y^2-6y+1\)

A parabola has a vertex of \((3, -2)\) and \(x\)-intercepts of \(0\) and \(6\). Find its equation.

A parabola has a vertex of\((-4, 1)\) and \(y\)-intercepts of \(-7\) and \(9\). Find its equation.

Sketch the graph of \(\dfrac{x^2}{9}+\dfrac{y^2}{36}=1\)

Sketch \(4x^2+9y^2=36\)

Graph \(x^2+9y^2+4x-54y+76=0\)

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

Graph the equation \(64x^2-16y^2=64\)

Graph \(4x^2-y^2+4y-20=0\)

Solve

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

Solve

\[\begin{aligned} 16x^2-4y^2&=64\\ x^2+y^2&=9\end{aligned}\]

Solve

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

The sum of the squares of two numbers is \(34\). The difference of their squares is \(16\). Find the two numbers.