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Question 109

The circle C C\,C has the equation x2+y2+kx−4y+h=0x^2 + y^2 + kx - 4y + h = 0x2+y2+kx−4y+h=0 where h h\,h and k k\,k are constants and k>0k>0k>0. Given that the point (1,5)(1, 5)(1,5) lies on CCC.

a.

Find the value of h h\,h in terms of kkk.

[2]
b.

Find the coordinates of the centre and the radius of C C\,C in terms of kkk.

[3]
c.

A straight line that passes through the point A(3,7)A(3, 7)A(3,7) is a tangent to the circle C C\,C at the point BBB. Find the exact length of the line AB AB\,AB in terms of kkk.

[5]
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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