Question 1
3 marks(a)
Write down the equation of the circle with centre and radius .
(b)
Write down the equation of the circle with centre and radius .
Equation of a Circle Practice Questions
Question 2
4 marksThe equation of a circle is (x−5)2+(y+2)2=49
(a)
Complete these statements.
The coordinates of the centre of the circle are ( , )
The radius of the circle is
(b)
Show that the point (1,1) lies inside the circle.
Question 0
3 marksPoints A(−2,7) and B(6,1) lie on a circle. AB is a diameter of the circle.
Work out the equation of the circle.
Question 0
7 marksA circle has equation (x−1)2+(y+3)2=25 and centre C.
The point P has coordinates (6,9).
PT and PS are the two tangents from P to the circle, touching it at T and S.
(a)
Show that P lies outside the circle.
(b)
Work out the length of PT.
(c)
Work out the area of quadrilateral PTCS.
Question 0
6 marksA circle has centre (0,0) and radius 13.
A straight line has equation y−x=7
Work out the coordinates of the two points where the circle and the straight line intersect.
Do not use trial and improvement.
You must show your working.
Question 0
5 marksA circle has equation (x−2)2+(y+1)2=25
The point P has coordinates (5,3).
(a)
Show that P lies on the circle.
(b)
Work out the equation of the tangent to the circle at P.
Give your answer in the form y=mx+c.
Question 0
6 marksYou may use a calculator for this question.
The equation of a circle is (x+1)2+(y−2)2=20
The equation of a line is 2x−y+3=0
The circle and the line intersect at two points, A and B.
(a)
Show that the x-coordinates of A and B satisfy the equation 5x2+6x−18=0
(b)
Work out the length of AB.
Give your answer to 3 significant figures.
Question 0
5 marksThe equation of a circle is (x−1)2+(y−3)2=8
The equation of a line is y=x+6
Show that the line is a tangent to the circle, and write down the coordinates of the point where they touch.
You must show your working.
Question 0
8 marksYou may use a calculator for this question.
A circle has centre C(−1,4) and radius 5.
The point A(3,7) lies on the circle.
AB is a chord of the circle, where B is the point (2,0).
(a)
Show that B lies on the circle.
(b)
M is the midpoint of AB.
Explain why CM is perpendicular to AB, and work out the length of CM.
Give your answer to 3 significant figures.
(c)
Work out the area of triangle ABC.
Question 0
8 marksA(−3,−1) and B(5,5) are the end points of a diameter of a circle.
(a)
Work out the equation of the circle.
(b)
Show that the point C(5,−1) lies on the circle.
(c)
Hence work out the area of triangle ABC.