Find the standard form of the parabola with focus (0, 12) and directrix with equation $x=-12.$

Convert the equation $y^2-2y+8x+25=0$ to the standard form for a parabola by completing the square.

Find the focus and directrix of the parabola with equation $x^2=-9y.$

Graph the parabola with equation $y^2=-5x.$

Find the vertex, focus, and directrix of the parabola with equation ${(x+2)}^2=-8(y-1).$

The base of a water slide is parabolic in shape and is 6 feet wide and 2 feet deep. Find the height of the slide 1 foot from its center.

Find an equation of the parabola with vertex $(3,-1)$ and directrix $x=-3.$

Foci: $(0,-2),(0,2)$ vertices: $(0,-4),(0,4)$

Foci: $(-2,0)(2,0);$ y-intercepts: $-5,5$

Major axis horizontal with length 18; minor axis of length 4; center (0, 0)

Graph the ellipse with equation $9x^2+y^2=9.$

Find the vertices and foci for the hyperbola with equation $49y^2-x^2=49.$

Graph the hyperbola with equation ${\displaystyle \frac{x^2}{49}}-{\displaystyle \frac{y^2}{4}}=1.$

Find the standard form of the equation of the hyperbola with foci $(0,-\sqrt{45}),(0,\sqrt{45})$ and vertices $(0,-6),(0,6).$

$y^2-x^2+2x=2$

$x^2-2x-4y^2-16y=19$

$x^2-9y^2=-16$

$x^2-x+4y+{\displaystyle \frac{1}{4}}=0$

$x^2+y^2+2x-6y=3$

$25x^2+4y^2=100$