Mathematics 9709 · AS & A Level · Coordinate geometry
Coordinate geometry — practice question
The figure depicts a circle $C$ with radius $r$, and every point on $C$ has $x > 0$ and $y > 0$. The smallest distance from any point on $C$ to the $x$-axis is $8$ units, while the smallest distance from any point on $C$ to the $y$-axis is $5$ units.
(a)[1]
Give the coordinates of the circle’s centre in terms of $r$.
(b)[3]
Since the distance from the origin to the centre of the circle is $15$ units, determine the value of $r$.
(c)[2]
The point on the circle that is furthest from the origin is labelled $P$. Find the gradient of the tangent to the circle at $P$.
Worked solution & mark scheme
This 6-mark question has a full step-by-step worked solution and mark scheme. One marking point: “The correct ordered pair is $(r+5,\,r+8)$.” …