The circle with equation x2+y2−6x+ky−7=0x^2 + y^2 - 6x + ky - 7 = 0x2+y2−6x+ky−7=0 has radius 5.
Show that the equation of the circle can be written as
(x−3)2+(y+k2)2=k24+16. (x - 3)^2 + \left(y + \frac{k}{2}\right)^2 = \frac{k^2}{4} + 16. (x−3)2+(y+2k)2=4k2+16.Hence find the two possible values of the constant kkk.
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.