Mathematics 9709 · AS & A Level · Coordinate geometry

Coordinate geometry — practice question

The curve is defined by $y = x^2 - x + 3$ and the line is defined by $y = 3x + a$, where $a$ is a constant.
(a)[1]

Show that the $x$-coordinates of the points of intersection of the line and the curve satisfy the equation $x^2 - 4x + (3 - a) = 0$.

(b)[2]

For the case in which the line cuts the curve at two points, you are told that one point of intersection has $x$-coordinate $-1$. Find the $x$-coordinate of the other point of intersection.

(c)[4]

For the case where the line is tangent to the curve at a point $P$, determine the value of $a$ and the coordinates of $P$.

Worked solution & mark scheme

This 7-mark question has a full step-by-step worked solution and mark scheme. One marking point: “Rearrange into the quadratic $x^2-4x+(3-a)=0$.” …

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