Mathematics 9709 · AS & A Level · Coordinate geometry
Coordinate geometry — practice question
The equation of a straight line is $y = -2x + k$, where $k$ is a constant, while the curve is given by $y = \frac{2}{x - 3}$.
(i)[1]
Show that the $x$-coordinates of any points of intersection of the line and curve satisfy the equation $2x^2 - (6 + k)x + (2 + 3k) = 0$.
(ii)[3]
Find the two values of $k$ that make the line a tangent to the curve.
(iii)[6]
The two tangents, with the values of $k$ found in part (ii), touch the curve at points $A$ and $B$. Find the coordinates of $A$ and $B$, together with the equation of the line $AB$.
Worked solution & mark scheme
This 10-mark question has a full step-by-step worked solution and mark scheme. One marking point: “Quadratic form rearranged correctly” …