Respuesta :

altavistard

Answer:

(-6, 7) is NOT on the given circle

Step-by-step explanation:

Write out the standard equation of a circle with center at (h, k) and radius r:

(x - h)^2 + (y - k)^2 = r^2, where (h, k) is the center and r is the radius.

Substituting 2 for h and -9 for k, and 5 for r, we get

(x - 2)^2 + (y + 9)^2 =5^2

Now determine whether or not the point (-6, 7) is on this circle:

Substituting -6 for x and 7 for y, we get:

(-6 - 2)^2 + (7 + 9)^2 =5^2    Is this true or false?

64 + 256 = 225?  NO.  Thus, (-6, 7) is NOT on the given circle.

ajeigbeibraheem

The point (-6, 7) is not given on the circle with a radius of 5 and center (2, -9).

What is the equation of a circle?

The general equation of a circle is used to determine the validity of a (xy) location or point on the circle.

It can be expressed as:

(x - h)² + (y - k)² = r²

where;

  • (h,k) = refers to the center
  • r = radius

by replacing the;

  • center (h) = 2
  • k = -9
  • r = 5

Then, (x - 2)² + (y - 9)² = 5²

Now, we are going to point xy with x = -6 and y = 7 in the above expression.

i.e.

(-6 - 2)² + (7 - 9)² = 5²

64 + 256 = 225

320 ≠ 225

Therefore, since the center of the circle is not equal to the radius of the circle, we can conclude that the point (-6, 7) is not given on the circle with a radius of 5 and center (2, -9).

Learn more about the equation of a circle here;
https://brainly.com/question/1506955

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