In the diagram, a circle centered at the origin, a right triangle, and the pythagorean theorem are used to derive the equation of a circle, x2 + y2 = r2. if the center of the circle were moved from the origin to the point (h, k) and point p at (x, y) remains on the edge of the circle, which could represent the equation of the new circle? (h + x)2 + (k + y)2 = r2 (x – h)2 + (y – k)2 = r2 (k + x)2 + (h + y)2 = r2 (x – k)2 + (y – h)2 = r2

Step-by-step explanation:

Here, the given equation of the circle,

Where r be the radius of the circle.

Since, after moving the circle the point P(x,y) is still present in the edge of the new circle,

Thus, the radius of the new circle will be also r.

Also, the radius be the distance from the center to a point on the edge of the circle,

The center of the new circle = (h,k)

⇒ The distance between the points (h,k) and (x,y) = r

⇒

⇒  

Since, (x,y) general representation of the points of the circle,

Hence, this is the required equation of the new circle.

question: how many people can she serve?

answer: she can serve 16.66666667 people. so she can only give 16 people a complete serving.

question: does she have enough ice cream for her guests?

answer: no. explanation: she only has enough for 16 people to have a full serving. however, she can give a 17th person a partial serving.

step-by-step explanation: