AS Maths - Core 1 - Solomon Worksheets - Circles - Worksheet C - Mixed 'Exam-style' Questions

Practice worksheets for Core 1 topic cirles

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Preview of AS Maths - Core 1 - Solomon Worksheets - Circles - Worksheet C - Mixed 'Exam-style' Questions

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C1 CIRCLES Worksheet C
1 A circle has the equation x2 + y2 - 8x + 7 = 0.
a Find the coordinates of the centre of the circle. (2)
b Find the radius of the circle. (2)
2 A circle has the equation x2 + y2 - 6x + 2y - 15 = 0.
a Find the coordinates of the centre of the circle. (2)
b Find the radius of the circle. (1)
c Show that the tangent to the circle at the point (7, 2) has equation
4x + 3y - 34 = 0. (4)
3 A circle has the equation x2 + y2 + 6x - 8y + 21 = 0.
a Find the coordinates of the centre and the radius of the circle. (3)
The point P lies on the circle.
b Find the greatest distance of P from the origin. (2)
4 y
x2 + y2 = 50 A
O x
C
B
The diagram shows the circle with equation x2 + y2 = 50 and the tangents to the circle
at the points A (5, 5) and B (1, -7).
a Find an equation of the tangent to the circle at A. (3)
b Show that the tangent to the circle at B has the equation
x - 7y - 50 = 0. (3)
c Find the coordinates of the point C where the tangents to the circle at A and B intersect. (2)
5 Circle C1 has the equation x2 + y2 - 2ay = 0, where a is a positive constant.
a Find the coordinates of the centre and the radius of C1. (4)
Circle C2 has the equation x2 + y2 - 2bx = 0, where b is a constant and b > a.
b Sketch C1 and C2 on the same diagram. (4)
6 The circle C has the equation x2 + y2 + 2x - 14y + 30 = 0.
a Find the coordinates of the centre of C. (2)
b Find the radius of C, giving your answer in the form k 5 . (2)
c Show that the line y = 2x - 1 is a tangent to C and find the coordinates of the point
of contact. (4)
Solomon Press

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C1 CIRCLES Worksheet C continued
7 The circle C has equation x2 + y2 - 6x - 12y + 28 = 0.
a Find the coordinates of the centre of C. (2)
The line y = x - 2 intersects C at the points A and B.
b Find the length AB in the form k 2 . (6)
8 The circle C has centre (8, -1) and passes through the point (4, 1).
a Find an equation for C.…read more

Comments

daviesg

A great set of questions on cirle equations showing a range of difficulty for core 1.  Answers would be good to check results.

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