+0

# Unit 5 and 6 Conic Sections and Modeling with Geometry

0
2
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​ .

May 31, 2024

#2
+759
+1

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! :)

May 31, 2024
#3
+759
+1

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! :)

May 31, 2024