Review All Conics

Review All Conics

Parabolas - Ellipse - Hyperbolas - circles

Multiple Choice

The focus is always inside the parabola.

• true
• false

Multiple Choice

What is the green dashed line called?

• directrix

• parabola

• axis of symmetry

• asymptote

Multiple Choice

What number would go in the blank?

• -2

• -4

• -8

• -16

Multiple Choice

Which direction does this parabola open?

• Up

• Down

• Left

• Right

Multiple Choice

Given this directrix and vertex, what would the equation of the parabola be?

• (y-2)² = 12(x-1)

• (y-2)² = 6(x-1)

• (x-1)² = 12(y-2)

• (x-1)² = 6(y-2)

Multiple Choice

(x+3)² = 4(y+5)

What is the equation of the directrix?

• x = 4

• x = 2

• y = -4

• y = -6

Multiple Choice

(y-4)² = -8(x+1)

What are the coordinates for the focus?

• (1,4)

• (-1,6)

• (-1,2)

• (-3,4)

Multiple Choice

$$x^2+4x-4y=0$$  Put into vertex form

• $$\left(x+2\right)^2=4\left(y+1\right)$$  

• $$\left(x-2\right)^2=4\left(y-1\right)$$  

Multiple Choice

Center?

• (-3 , 2)

• (3 , -2)

• (12 , 16)

• (√12 , 4)

Multiple Choice

What are the vertices of the ellipse?

• (0, 0)

• (7, 1) and (-1, 1)

• (3, -5) and (3, 7)

• (3, 1)

Multiple Choice

Find the foci of this ellipse?

• (8, -1), (0, -1)

• (4±√7, -1)

• (4, 3), (4, -5)

• (4, -1)

Multiple Choice

Write an equation for the ellipse with each set of characteristics. Then answer the question.

Vertices ( -7, -3), (13, - 3)

foci ( - 5, -3 ) , (11 , -3)

what is the a and b value of the ellipse?

• a = 10 , b = 6

• a = 6 , b = 10

• a = 36 , b = 100

• a = 100 , b = 36

Multiple Choice

The foci of an ellipse are located at (-2, 3) & (2, 3), where is the center?

• (0, 3)

• (3, 0)

• (-2, 0)

• (2, 0)

Multiple Choice

Standard Equation?

$$9x^2+4y^2-54x+40y+37=0$$  

Multiple Choice

Vertices ?

• (-15 , 2) ; (9 , 2)

• (15 , 2) ; (-9 , 2)

• (-15 , -2) ; (9 , -2)

• (15 , -2) ; (-9 , -2)

Multiple Choice

Coordinates of the Vertices?

• (0 , 5) ; (0 , -5)

• (0 , 9) ; (0 , -9)

• (5 , 0) ; (-5 , 0)

• (9 , 0) ; (-9 , 0)

Multiple Choice

Coordinates of the center?

• (0 , 0)

• (5 , 9)

• (9 , 5)

• (81 , 25)

Multiple Choice

Equation ?

Multiple Choice

Equation ?

Multiple Choice

write the following into vertex form:

$$-x+4y^2-2x-16y+11=0$$  

• $$\frac{\left(y-2\right)^2}{1}-\frac{\left(x+1\right)^2}{4}=1$$  

• $$\frac{\left(x+1\right)^2}{4}-\frac{\left(y-2\right)^2}{1}=1$$  

Multiple Choice

What are the center and radius for the circle: $$\left(x+2\right)^2+\left(y-6\right)^2=9$$  ?

• Center:  (-2, 6), Radius:  9

• Center:  (-2, 6), Radius:  3

• Center:  (2, -6), Radius:  3

• Center:  (2, -6), Radius:  9

Multiple Choice

What is the equation of the circle whose center is at $\left(-3,0\right)$ and $r=11$ ?

• $$(x-3)^2+y^2=11$$

• $$(x+3)^2+y^2=11$$

• $$(x-3)^2+y^2=121$$

• $$(x+3)^2+y^2=121$$

Multiple Choice

What is the center and radius of the circle given the equation $$x^2+y^2=7$$ ?

• $$C\left(0,0\right);\ r=\sqrt{7}$$

• $$C\left(0,0\right);\ r=7$$

• $$C\left(2,2\right);\ r=\sqrt{7}$$

• $$C\left(1,1\right);\ r=7$$

Multiple Choice

What is the equation of the given circle?

• $$(x-1)^2+(y-3)^2=16$$

• $$(x-3)^2+(y-1)^2=16$$

• $$(x-1)^2+(y+3)^2=16$$

• $$(x-1)^2+(y-3)^2=4$$

Multiple Choice

What is the equation of the given circle?

• $$(x+4)^2+(y+1)^2=9$$

• $$(x+4)^2+(y+1)^2=3$$

• $$(x-4)^2+(y-1)^2=9$$

• $$(x+4)^2+(y-1)^2=3$$

Multiple Choice

What is the standard form of the equation: $$x^2+y^2-10x+2y-10=0$$  ?

• $$\left(x-5\right)^2+\left(y+1\right)^2=16$$  

• $$\left(x-5\right)^2+\left(y+1\right)^2=10$$  

• $$\left(x-5\right)^2+\left(y+1\right)^2=6$$  

• $$\left(x-5\right)^2+\left(y+1\right)^2=36$$