50 Miscellaneous Parabolas Hyperbolas Ellipses Circles 40 30 20 10 20 30 40 50 10 20 30 40 50 10 20 30 40 50 10 20 30 40 50.

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Presentation transcript:

50 Miscellaneous Parabolas Hyperbolas Ellipses Circles

What is the center of the circle with the equation (x – 2) 2 + (y + 5) 2 = 9

(2, -5)

What is the radius of the circle with the equation (x – 1) 2 + (y – 3) 2 = 9

3

What is the standard form of the equation of a circle with center at the origin and a radius of 4?

x 2 + y 2 = 16

What is the standard form of the equation of a circle that has a diameter with endpoints (-2, 10) and (6, 4)?

(x – 2) 2 + (y – 7) 2 = 25

Find the center and the radius for the circle with the equation x 2 + y 2 – 4x +12y + 30 = 0

How many vertices do ellipses have?

4

If the foci of an ellipse are (0, 5) and (0, -5), is the major axis horizontal or vertical?

Vertical

In an ellipse, if a = 4 and b = 3, what is c?

Write the standard form of the equation of an ellipse with foci at (-4, 7) and (-4, -1), and whose major axis is 10 units long.

Find the coordinates of the center, the foci, and the vertices of the ellipse with the equation 4x 2 + 9y 2 -40x +36y +100 = 0

What is the relationship between a, b, and c for hyperbolas? (equation)

a 2 + b 2 = c 2

What are the names of the two axes for hyperbolas?

Transverse And Conjugate

Write the standard form of the equation of a hyperbola where a = 3 and the foci are at (0, 5) and (0, -5)

Write the standard form of the equation of a hyperbola with foci at (0, 8) and (0, -8) and vertices at (0, 6) and (0, -6)

The equation of a parabola has how many squared terms?

1

What variable represents the distance from the vertex of a parabola to the focus?

p

If a parabola has a directrix at y = 1 and a focus at (2, -3), what is the vertex of the parabola?

(2, -1)

Write the standard form of the equation of the parabola where the vertex is at (2, 3) and the focus is at (-5, 3)

(y - 3) 2 = -28(x - 2)

Find the vertex, the focus, the directrix, and the axis for the parabola with equation y 2 – 2y – 12x + 13 = 0

Vertex: (1, 1) Focus: (4, 1) Directrix: x = -2 Axis: y = 1

Which conic section has two vertices?

Hyperbola

What type of conic section is represented by the equation x 2 – 4y -6x +9 = 0 ?

Parabola

Which type of conic section is represented by the equation 4x 2 – 4y 2 + 5x – 6y +12 = 0?

Hyperbola

Write the standard form of the equation 4x 2 + 4y 2 + 8x + 16y + 4 = 0

(x+1) 2 + (y + 2) 2 = 4