6. Petra is given the equation (x-15) ^2 + (y+4) ^2=100 and identifies its graph as a circle whose center is (-15,4) and radius is 10. Has Petra made a mistake? Explain.

Answer:Yes, Petra has made a mistake

Step-by-step explanation:

Comparing Petra's given equation

(x-15) ² + (y+4) ²=100 to the general equation of a circle

(x-a) ² + (y-b) ² = r²

Where center is (a, b) and radius is r

Comparing both equation to know if Petra is correct

-a = - 15 i. e a = 15

-b = 4 i. e b = - 4

r² = 100

r = √100

r = 10

Based on the comparison, the center is (15,-4) and the radius is 10units which shows that Petra's value of the center of the circle is incorrect.

Therefore, Petra has made a mistake while calculating the center of the circle.