Sketch the graphs whose equations are: ${{(2x+11)}^{2}}+4{{y}^{2}}=121$ ${{(y-3)}^{2}}=10-2x$ \(

Question

Sketch the graphs whose equations are: ${{(2x+11)}^{2}}+4{{y}^{2}}=121$ ${{(y-3)}^{2}}=10-2x$ ${{y}^{2}}+4y-4{{x}^{2}}+8x+9=0$ ${{y}^{2}}+4{{x}^{2}}-4x=7$ $\frac{{{y}^{2}}}{7}-\frac{{{x}^{2}}}{5}=1$

Accepted Answer

(a) Circle: centre $\left(-\dfrac{11}{2},0\right)$, radius $\dfrac{11}{2}$, intercepts $(-11,0)$ and $(0,0)$ (b) Ellipse: centre $\left(\dfrac12,0\right)$, semi-axes $\sqrt2$ and $2\sqrt2$, $x$-intercepts $\left(\dfrac12\pm\sqrt2,0\right)$, $y$-intercepts $(0,\pm\sqrt7)$ (c) Left-opening parabola: vertex $(5,3)$, axis $y=3$, $x$-intercept $\left(\dfrac12,0\right)$, $y$-intercepts $(0,3\pm\sqrt{10})$ (d) Vertical hyperbola: centre $(0,0)$, vertices $(0,\pm\sqrt7)$, asymptotes $y=\pm\sqrt{\dfrac75}\,x$, no $x$-intercepts (e) Horizontal hyperbola: centre $(1,-2)$, vertices $\left(-\dfrac12,-2\right)$ and $\left(\dfrac52,-2\right)$, asymptotes $y=-2x$ and $y=2x-4$, $x$-intercepts $\left(1\pm\dfrac{\sqrt{13}}{2},0\right)$, no $y$-intercepts

HCI Tutorial 2A Question 2

HCI Tutorial 2A Question 2

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