Question

Choose the correct conic section to fit the equation (x-8)^2+(y-12)^2=25

a. Circle
b. Eclipse
c. Parabola
d. Hyperbola

Answer 1

Answer: a. Circle

Explanation:

Given equation:
`(x-8)^2+(y-12)^2=25` which is equivalent to
`(x-8)^2+(y-12)^2=5^2`

This equation is of the form
`(x-h)^2+(y-k)^2=r^2` which is the standard equation of a circle centered at (h,k) with radius r.

On comparing given equation to the standard equation of circle we have, h=8 and k=12 and r =2.

Therefore, given equation represent a circle centered at (8,12) and radius=5 units.