A circle has equation
$(x - 4)^2 + (y + 4)^2 = 9$
What is the area of the circle?
Circle your answer. - AQA - A-Level Maths Pure - Question 1 - 2018 - Paper 3
Question 1
A circle has equation
$(x - 4)^2 + (y + 4)^2 = 9$
What is the area of the circle?
Circle your answer.
Worked Solution & Example Answer:A circle has equation
$(x - 4)^2 + (y + 4)^2 = 9$
What is the area of the circle?
Circle your answer. - AQA - A-Level Maths Pure - Question 1 - 2018 - Paper 3
Step 1
Identify the Circle's Radius
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Answer
The equation of the circle is in the form
(x−h)2+(y−k)2=r2
where (h,k) is the center and r is the radius. Comparing with the given equation, we see that:
The center is at (4,−4)
The right-hand side is 9, which means:
\Rightarrow r = 3$$
Step 2
Calculate the Area of the Circle
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Answer
The area of a circle is calculated using the formula:
A=πr2
Substituting in the radius:
= 9\pi$$
Step 3
Select the Correct Option
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Answer
Based on the calculations, the area of the circle is:
9π
The answer to circle is 9π.
