Unit 5 and 6 Conic Sections and Modeling with Geometry

Question

0

28

3

+4

1. A plane intersects one cone of a double-napped cone such that the plane is parallel to the generating line.

ellipse

hyperbola

parabola

circle

2.

A circle is centered at (11, −9) and has a radius of 12.

What is the equation of the circle?

Enter the equation using lowercase variables x and y in the box.

3.

The equation of a circle is (x−2)2+(y−16)2=169 .

What is the circle's radius?

Enter your answer in the box.

aakita May 31, 2024

NotThatSmart · Answer 1 · 2024-05-31T07:18:19

2. The equation of a circle is $(x – h)^2 + (y – k)^2 = r^2$ where $(h,k)$ is the center of the circle and $r$ is the radius.

Now, we can just plug in the information we were already given in the equestion.

If the center is (11, -9), we have $h=11$ and $k=-9$ and radius of 12.

We have $(x-11)^2+(y+9)^2 = 144$ .

Thanks! :)

NotThatSmart · Answer 2 · 2024-05-31T07:20:43

3. As I said in question #2, we have $(x – h)^2 + (y – k)^2 = r^2$ where r is the radius.

This means we have $r^2 =169$ , which just gives us $r = \sqrt{169} = 13$ . So the radius is 13.

Note, the radius can't be -13 because the length or radius can't be negative!

Thanks! :)