Mathematics 9709 · AS & A Level · Coordinate geometry

Coordinate geometry — practice question

The circle is given by the equation $x^2 + y^2 + 6x - 2y - 26 = 0$.
(a)[4]

Find the coordinates of the centre of the circle and the radius. Hence find the coordinates of the point lowest on the circle.

(b)[6]

Find the set of values of the constant $k$ for which the line with equation $y = kx - 5$ meets the circle at two distinct points.

Worked solution & mark scheme

This 10-mark question has a full step-by-step worked solution and mark scheme. One marking point: “By completing the square, this can be written as $(x+3)^2+(y-1)^2=36$.” …

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