Equation of a circle worksheet
10 GCSE practice questions with answers, free to print. Every sheet is generated, so you can make a fresh one whenever you need it.
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2 marks
(a)
A circle has centre \(O\), the origin, and radius \(18\).
Write down the equation of the circle.
(b)A different circle has equation \(x^2 + y^2 = 196\)
Write down the radius of this circle.
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3 marks
The circle \(C\) has equation \(x^2 + y^2 = 9\)
(a)Write down the coordinates of the two points where \(C\) crosses the \(y\)-axis.
(b)State the coordinates of the point where \(C\) crosses the negative \(x\)-axis.
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3 marks
A circle has centre the origin and equation \(x^2 + y^2 = 52\)
(a)Calculate the radius of the circle.
Give your answer in the form \(a\sqrt{b}\), where \(a\) and \(b\) are integers and \(b\) is as small as possible.
(b)Calculate the radius correct to 1 decimal place.
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3 marks
The circle \(C\) has equation \(x^2 + y^2 = {rsq}\)
Does the point \(({px}, {py})\) lie inside \(C\), on \(C\), or outside \(C\)?
You must show your working.
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3 marks
A circle has centre \(O\), the origin, and passes through the point \((-12, 5)\).
(a)Find the equation of the circle.
(b)Write down the radius of the circle.
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3 marks
The point \((-5, k)\) lies on the circle \(x^2 + y^2 = 169\)
Given that \(k\) is positive, work out the value of \(k\).
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2 marks
(a)
A circle has centre \(O\), the origin, and radius \(15\).
Write down the equation of the circle.
(b)A different circle has equation \(x^2 + y^2 = 400\)
Write down the radius of this circle.
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3 marks
The circle \(C\) has equation \(x^2 + y^2 = 81\)
(a)Write down the coordinates of the two points where \(C\) crosses the \(y\)-axis.
(b)State the coordinates of the point where \(C\) crosses the negative \(x\)-axis.
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3 marks
A circle has centre the origin and equation \(x^2 + y^2 = 180\)
(a)Work out the radius of the circle.
Give your answer in the form \(a\sqrt{b}\), where \(a\) and \(b\) are integers and \(b\) is as small as possible.
(b)Work out the radius correct to 1 decimal place.
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3 marks
The circle \(C\) has equation \(x^2 + y^2 = {rsq}\)
Does the point \(({px}, {py})\) lie inside \(C\), on \(C\), or outside \(C\)?
You must show your working.
Answers
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(a) \(x^2 + y^2 = 324\)
(b) \(14\) -
(a) \((0, 3)\) and \((0, -3)\)
(b) \((-3, 0)\) -
(a) \(2\sqrt{ 13 }\)
(b) \(7.2\) - {verdict:cap}
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(a) \(x^2 + y^2 = 169\)
(b) \(13\) - \(12\)
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(a) \(x^2 + y^2 = 225\)
(b) \(20\) -
(a) \((0, 9)\) and \((0, -9)\)
(b) \((-9, 0)\) -
(a) \(6\sqrt{ 5 }\)
(b) \(13.4\) - {verdict:cap}