<p>A curve $C$ has equation ${{y}^{2}}=4a\left( a-x \right)$ for some positive constant $a$.</p>
<ol class="i-list"><li><div class="list-item-content"><span class="list-item-text">Describe a sequence of transformations that map ${{y}^{2}}=x$ to $C$, giving your answers in terms of $a$.</span></div></li><li><div class="list-item-content"><span class="list-item-text">Sketch $C$, labelling the coordinates of the axial intercepts in terms of $a$.</span></div></li><li><div class="list-item-content"><span class="list-item-text">Express the distance between the origin and an arbitrary point $\left( x,y \right)$ on $C$ in terms of $x$ and $a$. Hence, state, in terms of $a$, the equation of a line such that any point on $C$ is equidistance from this line and the origin $O_{{}}^{{}}$.</span></div></li></ol>

A curve $C$ has equation ${{y}^{2}}=4a\left( a-x \right)$ for some positive constant $a$.

Describe a sequence of transformations that map ${{y}^{2}}=x$ to $C$, giving your answers in terms of $a$.

Sketch $C$, labelling the coordinates of the axial intercepts in terms of $a$.

Express the distance between the origin and an arbitrary point $\left( x,y \right)$ on $C$ in terms of $x$ and $a$. Hence, state, in terms of $a$, the equation of a line such that any point on $C$ is equidistance from this line and the origin $O_{{}}^{{}}$.

Graphing Techniques Tutorial Q1

Graphing Techniques Tutorial Q1

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