Photo AI

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 Mechanics - Question 1 - 2018 - Paper 3

Question icon

Question 1

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 Mechanics-Question 1-2018-Paper 3.png

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 Mechanics - Question 1 - 2018 - Paper 3

Step 1

Determine the radius of the circle

96%

114 rated

Answer

The equation of the circle can be compared to the general form (x−h)2+(y−k)2=r2(x - h)^2 + (y - k)^2 = r^2, where (h,k)(h, k) is the center and rr is the radius. From the given equation, we see that:

  • The center is at (4,−4)(4, -4).
  • The term on the right side is 99, which means r2=9r^2 = 9. Thus, the radius rr is:

r=extsqrt(9)=3r = ext{sqrt}(9) = 3

Step 2

Calculate the area of the circle

99%

104 rated

Answer

The area AA of a circle is given by the formula:

A=extπr2A = ext{π}r^2

Substituting the radius we found:

A=extπ(32)=extπimes9=9extπA = ext{π}(3^2) = ext{π} imes 9 = 9 ext{π}

Step 3

Select the answer

96%

101 rated

Answer

Based on the choices provided (3π, 9π, 16π, 81π), the correct answer is:

9π

Join the A-Level students using SimpleStudy...

97% of Students

Report Improved Results

98% of Students

Recommend to friends

100,000+

Students Supported

1 Million+

Questions answered

;