# Lesson 13

Intersection Points

### 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.

A:

$$y-3=x-2$$

B:

$$4x+y=5$$

C:

$$y=5x-13$$

D:

$$x^2+y^2=13$$

E:

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

F:

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

G:

$$y=x^2-7$$

### 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 $$\ell$$ .

### Solution

(From Unit 6, Lesson 12.)

### Problem 5

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

### Solution

(From Unit 6, Lesson 12.)

### Problem 6

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

A:

$$y=\frac32 x +8$$

B:

$$3x - 2y = 2$$

C:

$$3x + 2y = 10$$

D:

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

E:

$$y=\frac32 x$$

### Solution

(From Unit 6, Lesson 11.)

### Problem 7

Select the line parallel to $$3x - 2y = 10$$.

A:

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

B:

$$6x + 4y =\text -20$$

C:

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

D:

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

### Solution

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