The circle C C\,C has the equation x2+y2+8x−4y+k=0x^2 + y^2 + 8x - 4y + k = 0x2+y2+8x−4y+k=0 where k k\,k is a constant. Given that the point (1,5)(1, 5)(1,5) lies on CCC.
Find the value of kkk.
Find the coordinates of the centre and the radius of CCC.
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 ABABAB.
143 exam-style questions on OCR A Level Maths 1.3 Coordinate Geometry in the x-y Plane, covering 1.3.1 Straight lines, 1.3.2 Parallel and perpendicular lines, 1.3.3 Straight line models, 1.3.4 Coordinate geometry of a circle, 1.3.5 Centre and radius by completing the square, 1.3.6 Circle properties, 1.3.7 Parametric equations of curves (A-level only), 1.3.8 Parametric equations in context (A-level only), and 1.3 Coordinate Geometry in the x-y Plane. Each one has a worked solution and a mark scheme showing where the marks go.