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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.

 May 31, 2024
 #2
avatar+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
avatar+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

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