Question

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 1

Answer:Yes, Petra has made a mistake

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.