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Question 13

The circle C C\,C has the equation

x2+y2+2x−6y+k=0, x^2+y^2+2x-6y+k=0, x2+y2+2x−6y+k=0,

where k k\,k is a constant. Given that the point (3,5)(3,5)(3,5) lies on CCC.

a.

Find the value of kkk.

[2]
b.

Find the coordinates of the centre and the radius of CCC.

[3]
c.

A straight line that passes through the point A(3,8)A(3,8)A(3,8) is tangent to the circle C C\,C at the point BBB.

Find the exact distance from A A\,A to the centre of CCC.

[2]
d.

Hence find the exact length of the line ABABAB.

[3]
Markscheme

Circles Questions

  1. A Level
  2. /Maths
  3. /Circles

292 exam-style questions on Edexcel A Level Maths Circles, covering 6.1 Midpoints and Perpendicular Bisectors, 6.2 Equation of a Circle, 6.3 Intersections of Straight Lines and Circles, 6.4 Use Tangent and Chord Properties, and 6.5 Circles and Triangles. Each one has a worked solution and a mark scheme showing where the marks go.

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