Problem 1: Find the equation of the line passing through the points $(-3,-16)$ and $(4,5)$. Enter your answer in "$y = mx + b$" form.

Problem 2: The equation of the line passing through $(1,8)$ and $(5,6)$ can be expressed in the form \[\frac{x}{a} + \frac{y}{b} = 1.\] Find $a$.

Problem 3: The graph of the equation \[4x^2 - 12x + 4y^2 + 56y - 471 = 0\] is a circle. Find the radius of the circle.

Problem 4: For some positive real number $r$, the line $x + y = r$ is tangent to the circle $x^2 + y^2 = r$. Find $r$.

Problem 5: The circles $x^2 + y^2 = 4$ and $(x - 2)^2 + (y - 3)^2 = 7$ intersect in two points $A$ and $B$. Find the slope of $\overline{AB}$.

Problem 6: Find the center of the circle passing through the points $(-1,0)$, $(1,0)$, and $(3,1)$. Express your answer in the form "$(a,b)$."

Problem 7: A line with slope 3 is 2 units away from the origin. Find the area of the triangle formed by this line and the coordinate axes.

Problem 8: Find the maximum value of $y/x$ over all real numbers $x$ and $y$ that satisfy \[(x - 3)^2 + (y - 3)^2 = 6.\]

Problem 9: Let $P = (5,1)$, and let $Q$ be the reflection of $P$ over the line $y = \frac{1}{2} x + 2$. Find the coordinates of $Q$.

Confusedperson
Jul 2, 2018