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?

Blank coordinate plane with grid, origin O. Horizontal and vertical scale negative 10 to 10 by 2’s.

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.

graph of the parabola with focus at 3 comma 4 and directrix  y =2, and the line given by y = 4.

Problem 4

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

graph on line L, y intercept of 7 and slope of -1 over 2
(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 \((2,5)\).

(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:

\(y=\frac32 x\)

(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:

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

(From Unit 6, Lesson 10.)

Problem 8

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

(From Unit 6, Lesson 5.)