Write an equation of the line that passes through \((1,3)\) and has a slope of \(\frac{5}{4}\).

A parabola has focus \((3,\text{-}2)\) and directrix \(y=2\). The point \((a,\text{-}8)\) is on the parabola. How far is this point from the focus?

Write an equation for a parabola with each given focus and directrix.

1. focus: \((5, 2)\); directrix: \(x\)-axis
2. focus: \((\text{-}2, 3)\); directrix: the line \(y=7\)
3. focus: \((0,7)\); directrix: \(x\)-axis
4. focus: \((\text{-}3, \text- 4)\); directrix: the line \(y=\text-1\)

A parabola has focus \((\text{-}1,6)\) and directrix \(y=4\). Determine whether each point on the list is on this parabola. Explain your reasoning.

1. \((\text{-}1,5)\)
2. \((1 ,7)\)
3. \((3, 9)\)

Select the center of the circle represented by the equation \(x^2 + y^2 - 8x + 11y - 2 = 0\).