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Describe fully the graph which has the equation $x^2 + y^2 = 9$. - OCR - GCSE Maths - Question 17 - 2017 - Paper 1

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Question 17

Describe-fully-the-graph-which-has-the-equation-$x^2-+-y^2-=-9$.-OCR-GCSE Maths-Question 17-2017-Paper 1.png

Describe fully the graph which has the equation $x^2 + y^2 = 9$.

Worked Solution & Example Answer:Describe fully the graph which has the equation $x^2 + y^2 = 9$. - OCR - GCSE Maths - Question 17 - 2017 - Paper 1

Step 1

Circle

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Answer

The graph of the equation x2+y2=9x^2 + y^2 = 9 represents a circle. This is evident since it is in the standard form of a circle's equation, which is (x−h)2+(y−k)2=r2(x - h)^2 + (y - k)^2 = r^2, where ((h, k)) is the center of the circle and (r) is the radius.

Step 2

Center and Radius

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Answer

From the equation, we can determine that the center of the circle is at the origin ((0, 0)), and the radius (r) can be found using (r = \sqrt{9} = 3). Thus, the circle has a radius of 3.

Step 3

Shape

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Answer

In summary, the graph is a circle, centered at the origin ((0, 0)) with a radius of 3. It is a closed and symmetrical shape.

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