Given that $k$ is a positive constant, sketch the curve $C$ , defined by the equation \(y=\

Question

Given that $k$ is a positive constant, sketch the curve $C$ , defined by the equation $y=\frac{2k{{x}^{2}}+\left( k+2 \right)x+3}{2x+1}$ , giving the equations of the asymptotes and the coordinates of any points of intersection with the x$x$- and $y$-axes, in terms of $k$ .[4] Given that the oblique asymptote of the curve $C$ is parallel to the line $y=x$, state the value of $k$.[1] Hence find the range of values of $a$ if the line $y=-x+a$ does not intersect the curve $C$, giving your answer in exact form.[3]

Accepted Answer

(i) asymptotes $x=-\dfrac12$ and $y=kx+1$, $y$-intercept $(0,3)$, and $x$-intercepts $\left(\dfrac{-(k+2)\pm\sqrt{k^2-20k+4}}{4k},0\right)$ for $0<k\leq10-4\sqrt6$ or $k\geq10+4\sqrt6$ (ii) $k=1$, and $-2\sqrt2<a<2\sqrt2$

2017 JJC Promo Q7

2017 JJC Promo Q7

Video Solution:

Solution:

Solution locked