# Lesson 13

Intersection Points

- Let’s look at how circles and parabolas interact with lines.

### Problem 1

Graph the equations \((x-2)^2+(y+3)^2=36\) and \(x = 2\). Where do they intersect?

### Problem 2

Select **all** equations for which the point \((2,\text- 3)\) is on the graph of the equation.

\(y-3=x-2\)

\(4x+y=5\)

\(y=5x-13\)

\(x^2+y^2=13\)

\((x-2)^2+(y-(\text- 3))^2=25\)

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

\(y=x^2-7\)

### Problem 3

The image shows a graph of the parabola with focus \((3,4)\) and directrix \(y=2\), and the line given by \(y=4\). Find and verify the points where the parabola and the line intersect.

### Problem 4

Here is a line \(\ell\). Write equations for and graph 4 different lines perpendicular to \(\ell\) .

### Problem 5

Write an equation whose graph is a line perpendicular to the graph of \(y=4\) and which passes through the point \((2,5)\).

### Problem 6

Select **all** lines that are perpendicular to \(y-4 = \text-\frac{2}3 (x+1)\).

\(y=\frac32 x +8\)

\(3x - 2y = 2\)

\(3x + 2y = 10\)

\(y-2 = \text-\frac{2}3 (x-1)\)

\(y=\frac32 x\)

### Problem 7

Select the line parallel to \(3x - 2y = 10\).

\(y-1 = \frac32 (x+6)\)

\(6x + 4y =\text -20\)

\(y =\text- \frac{3}2 x + 2\)

\(y-4 = \frac23 (x+1)\)

### Problem 8

Explain how you could tell whether \(x^2+bx+c\) is a perfect square trinomial.