1.1 Algebra and functions

85%

The curve $C\,$ has the equation $y=2x+kx∈R,x≠0\displaystyle y = \frac{2}{x} + k \quad x \in \mathbb{R}, x \neq 0$

The line $L\,$ has the equation $y = - 3 x + 2$

Show that the $x$ -coordinate of any point of intersection of $L\,$ with $C\,$ is given by a solution of the equation

3x^2 + (k - 2)x + 2 = 0

[3]

Hence find the exact values of $k\,$ for which $L\,$ is a tangent of $C$ .

[3]

1.1 Algebra and functions Questions

85%

The curve $C\,$ has the equation $y=2x+kx∈R,x≠0\displaystyle y = \frac{2}{x} + k \quad x \in \mathbb{R}, x \neq 0$

The line $L\,$ has the equation $y = - 3 x + 2$

Show that the $x$ -coordinate of any point of intersection of $L\,$ with $C\,$ is given by a solution of the equation

3x^2 + (k - 2)x + 2 = 0

[3]

Hence find the exact values of $k\,$ for which $L\,$ is a tangent of $C$ .

[3]