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Find the value of \(k\) if the point \((1,2)\) lies on the curve \((k-10) x^{2}+y^{2}-(k-7) x-(3 k-27) y+11=0\)
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The sketch below shows the grpahs of $f(x)=2x+3$ and $g(x)=-2x^2+14x+k$. C is any point on $f$ and D any point of $g$, such that CD is parallel to the y-axis. k is the value such taht C lies above D. In the sketch $\mathrm{A}(2 ; 3)$ and $\mathrm{B}(-1 ; 6)$ lie on the circle with midpoint $\mathrm{M}(\mathrm{c} ; \mathrm{d})$ $M$ is also a point on the line given by $2 x+5 y+$ $1=0$ The sketch below represents the graphs of two parabolas, $f$ and $g$. $f(x)=\dfrac{1}{2}x^2-8$. The turning point of $g$ is C(2;9) and the y-intercept of $g$ is A(0;5). B and D are the x-intercepts of $f$ and $g$ respectively Determine the area of the region bounded by the curve defined by \(y=x^{2}-4\) and the lines \(y=0\) and \(x=4\), as shown in the diagram below. The sketch shows the lines $2 y-3 x=-20$ and $y=k x+$ $p$ with $\theta=60,26^{\circ}$. In the sketch below you are given the coordinates of $\mathrm{A}$ $(0 ; 6), \mathrm{B}(4 ;-2)$ and $\mathrm{C}(3 k ; k)$. In the circle $C(1 ; 2)$ and $\mathrm{A}(0 ; 4):$ Determine the following:
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Grade 12 - Paper 1 - The graph of $g(x)=a x^{3}+b x^{2}+c x$, a cubic function having a $y$ -intercept of 0, is drawn below. The $x$ -coordinates of the turning points of $g$ are $-1$ and 2 . Grade 12 - Paper 1 - The graph of $f(x)=3^{-x}$ is sketched below. $A$ is the $y$ -intercept of $f$. $\mathrm{B}$ is the point of intersection of $f$ and the line $y=9$.
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asked May 12, 2020 in Mathematics by MathsGee Platinum (122,714 points) | 258 views

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