Practice section 1 of 2

Sketch the curves (a) $y^2-6x=12$ and (b) $x^2+4(y+1)=0$, and state the line(s) of symmetry.

Write down one possible equation of the parabola shown in the diagram.

Write down the equation of the ellipse shown in the diagram.

Sketch the ellipses:

(a) $\dfrac{(x-1)^2}{4}+\dfrac{(y+2)^2}{9}=1$,

(b) $x^2+y^2-5x+y-\dfrac52=0$,

and state the line(s) of symmetry.

Sketch the hyperbolas:

(a) $\dfrac{x^2}{4}-y^2=1$,

(b) $\dfrac{(x+4)^2}{9}-\dfrac{(y-2)^2}{16}=1$,

and state the line(s) of symmetry.

Find the equation of the hyperbola shown below.