Find the standard form of the equation of the parabola with focus $(-10,0)$ and directrix $x=10.$

1. $y^2=-10x$

2. $y^2=-40x$

3. $x^2=-40y$

4. $y^2=40x$

Convert the equation $y^2-4y-5x+24=0$ to the standard form for a parabola by completing the square.

1. ${(y+2)}^2=5(x-4)$

2. ${(y-2)}^2=5(x-4)$

3. ${(y+2)}^2=-5(x-4)$

4. ${(y-2)}^2=5(x+4)$

Find the focus and directrix of the parabola with equation $x=7y^2.$

1. focus: $({\displaystyle \frac{1}{28}},0);$ directrix: $x=-{\displaystyle \frac{1}{28}}$

2. focus: $(0,{\displaystyle \frac{1}{28}});$ directrix: $y=-{\displaystyle \frac{1}{28}}$

3. focus: $({\displaystyle \frac{1}{28}},0);$ directrix: $x={\displaystyle \frac{1}{28}}$

4. focus: $({\displaystyle \frac{1}{7}},0)$ directrix: $x=-{\displaystyle \frac{1}{7}}$

Find the vertex, focus, and directrix of the parabola with equation ${(x-3)}^2=12(y-1).$

1. vertex: (3, 1); focus: (3, 4); directrix: $y=-2$

2. vertex: $(3,-1);$ focus: $(-3,2);$ directrix: $y=-4$

3. vertex: (3, 1); focus: $(3,-2);$ directrix: $x=4$

4. vertex: (1, 3); focus: (1, 6); directrix: $y=0$

The parabolic arch of a bridge has a 180-foot base and a height of 25 feet. Find the height of the arch 45 feet from the center of the base.

1. 12.5 ft

2. 6.25 ft

3. 16.7 ft

4. 18.75 ft

Find an equation of the parabola with vertex $(-2,1)$ and directrix $x=2.$

1. ${(y-1)}^2=-16(x+2)$

2. ${(y-1)}^2=16(x+2)$

3. ${(y+2)}^2=-16(x-1)$

4. ${(y+2)}^2=16(x-1)$

Foci: $(-3,0),(3,0);$ vertices: $(-5,0),(5,0)$

1. ${\displaystyle \frac{x^2}{9}}+{\displaystyle \frac{y^2}{16}}=1$

2. ${\displaystyle \frac{x^2}{25}}+{\displaystyle \frac{y^2}{16}}=1$

3. ${\displaystyle \frac{x^2}{9}}+{\displaystyle \frac{y^2}{25}}=1$

4. ${\displaystyle \frac{x^2}{16}}+{\displaystyle \frac{y^2}{25}}=1$

Foci: $(0,-3),(0,3);$ y-intercepts: $-7,7$

1. ${\displaystyle \frac{x^2}{49}}+{\displaystyle \frac{y^2}{40}}=1$

2. ${\displaystyle \frac{x^2}{9}}+{\displaystyle \frac{y^2}{49}}=1$

3. ${\displaystyle \frac{x^2}{9}}+{\displaystyle \frac{y^2}{40}}=1$

4. ${\displaystyle \frac{x^2}{40}}+{\displaystyle \frac{y^2}{49}}=1$

Major axis vertical with length 16; length of minor $\text{axis}=8;$ center: (0, 0)

1. ${\displaystyle \frac{x^2}{16}}+{\displaystyle \frac{y^2}{64}}=1$

2. ${\displaystyle \frac{x^2}{64}}+{\displaystyle \frac{y^2}{256}}=1$

3. ${\displaystyle \frac{x^2}{8}}+{\displaystyle \frac{y^2}{64}}=1$

4. ${\displaystyle \frac{x^2}{64}}+{\displaystyle \frac{y^2}{16}}=1$

Find the vertices and foci of the hyperbola with equation ${\displaystyle \frac{x^2}{121}}-{\displaystyle \frac{y^2}{4}}=1.$

1. vertices: $(-11,0),(11,0);$ foci: $(-2,0),(2,0)$

2. vertices: $(0,-1),(0,11);$ foci: $(-5\sqrt{5},0)(5\sqrt{5},0)$

3. vertices: $(-11,0),(11,0);$ foci: $(-5\sqrt{5},0)(5\sqrt{5},0)$

4. vertices: $(-2,0),(2,0);$ foci: $(-5\sqrt{5},0)(5\sqrt{5},0)$

Find the standard form of the equation of the hyperbola with foci $(0,-10),(0,10)$ and vertices $(0,-5),(0,5).$

1. ${\displaystyle \frac{y^2}{25}}-{\displaystyle \frac{x^2}{100}}=1$

2. ${\displaystyle \frac{y^2}{25}}-{\displaystyle \frac{x^2}{75}}=1$

3. ${\displaystyle \frac{x^2}{25}}-{\displaystyle \frac{y^2}{100}}=1$

4. ${\displaystyle \frac{x^2}{25}}-{\displaystyle \frac{y^2}{75}}=1$

$y^2-4x^2-2y-16x-19=0$

1. ${\displaystyle \frac{{(y-2)}^2}{4}}-{(x+4)}^2=1$

2. ${\displaystyle \frac{{(x-1)}^2}{4}}-{(y+2)}^2=1$

3. ${\displaystyle \frac{{(y-1)}^2}{4}}-{(x+2)}^2=1$

4. ${(x+2)}^2-{\displaystyle \frac{{(y-1)}^2}{4}}=1$

$4y^2-9x^2-16y-36x-56=0$

1. ${\displaystyle \frac{{(y-2)}^2}{4}}-{\displaystyle \frac{{(x+2)}^2}{9}}=1$

2. ${\displaystyle \frac{{(x-2)}^2}{4}}-{\displaystyle \frac{{(y+2)}^2}{9}}=1$

3. ${\displaystyle \frac{{(y-2)}^2}{9}}-{\displaystyle \frac{{(x+2)}^2}{4}}=1$

4. ${\displaystyle \frac{{(y+2)}^2}{9}}-{\displaystyle \frac{{(x-2)}^2}{4}}=1$

$3x^2+2y^2-6x+4y-1=0$

1. parabola

2. circle

3. ellipse

4. hyperbola

$x^2+2x+4y+5=0$

1. parabola

2. circle

3. ellipse

4. hyperbola

$4x^2-y^2+16x+2y+11=0$

1. parabola

2. circle

3. ellipse

4. hyperbola

$5y^2-3x^2+20y-6x+2=0$

1. parabola

2. circle

3. ellipse

4. hyperbola