Question
In the xy plane, a circle has center P(5,10) and intersects the x axis at a single point Q(5,0). What is the area of circle P? Express your answer in terms of pi
Answers
GPT 3.5
The radius of the circle is the distance between the center P(5, 10) and the point Q(5, 0) on the x-axis.
Using the distance formula, the radius r is given by:
r = sqrt((5 - 5)^2 + (0 - 10)^2) = sqrt((0)^2 + (-10)^2) = sqrt(100) = 10.
The area of a circle is given by the formula A = πr^2.
Substituting the value of the radius r = 10 into this formula, we get:
A = π(10)^2 = π(100) = 100π.
Therefore, the area of circle P is 100π.
Using the distance formula, the radius r is given by:
r = sqrt((5 - 5)^2 + (0 - 10)^2) = sqrt((0)^2 + (-10)^2) = sqrt(100) = 10.
The area of a circle is given by the formula A = πr^2.
Substituting the value of the radius r = 10 into this formula, we get:
A = π(10)^2 = π(100) = 100π.
Therefore, the area of circle P is 100π.