Conics Flashcards

1
Q

What is the equation of an ellipse in standard position?

A

x^2/a^2 + y^2/b^2 = 1

How well did you know this?
1
Not at all
2
3
4
5
Perfectly
2
Q

State an expression for the term “b^2” in the equation of an ellipse in standard position.

A

b^2=a^2(1-e)

How well did you know this?
1
Not at all
2
3
4
5
Perfectly
3
Q

At what points does an ellipse in standard position intersect the coordinate axes?

A

(+|- a, 0) and (0, +|-b)

How well did you know this?
1
Not at all
2
3
4
5
Perfectly
4
Q

What is the equation for the eccentricity e of an ellipse in standard position?

A

e = sqrt(1 - b^2/a^2)

How well did you know this?
1
Not at all
2
3
4
5
Perfectly
5
Q

How can an ellipse in standard position be obtained from the circle with equation x^2 + y^2 = a^2?

A

By a vertical scaling of factor b/a.

How well did you know this?
1
Not at all
2
3
4
5
Perfectly
6
Q

State the focus-directrix definition of a parabola.

A

PF = Pd

How well did you know this?
1
Not at all
2
3
4
5
Perfectly
7
Q

State the focus-directrix definition of an ellipse.

A

PF = ePd where 0

How well did you know this?
1
Not at all
2
3
4
5
Perfectly
8
Q

State the focus-directrix definition of an hyperbola.

A

PF = ePd, where e>1

How well did you know this?
1
Not at all
2
3
4
5
Perfectly
9
Q

What is the equation of an hyperbola in standard position?

A

x^2/a^2 - y^2/b^2 = 1

How well did you know this?
1
Not at all
2
3
4
5
Perfectly
10
Q

Give an equation for the term “b^2” in the equation of an hyperbola in standard position.

A

b^2 = a^2(e^2-1), where b>0.

How well did you know this?
1
Not at all
2
3
4
5
Perfectly
11
Q

Give an equation for the eccentricity e if an hyperbola in standard position.

A

e = sqrt(1 + b^2/a^2)

How well did you know this?
1
Not at all
2
3
4
5
Perfectly
12
Q

What is the vertex of a standard parabola?

A

The origin, (0,0)

How well did you know this?
1
Not at all
2
3
4
5
Perfectly
13
Q

What is the focus of a standard parabola?

A

(a,0)

How well did you know this?
1
Not at all
2
3
4
5
Perfectly
14
Q

What is the directrix of a standard parabola?

A

x = -a

How well did you know this?
1
Not at all
2
3
4
5
Perfectly
15
Q

A parabola in standard position always passes through which two points? (State the points in terms of a).

A

(a, +|- 2a)

How well did you know this?
1
Not at all
2
3
4
5
Perfectly
16
Q

What is the common centre of both an ellipse and hyperbola in standard position?

A

The origin, (0,0).

17
Q

What are the four vertices of a standard ellipse, in terms of a and b?

A

(+|-a, 0) and (0, +|-b).

18
Q

What are the common axes of symmetry of both an ellipse and hyperbola in standard position?

A

The coordinate axes.

19
Q

What are the foci of a standard ellipse?

A

(+|- ae, 0)

20
Q

What are the directrices of an ellipse in standard position?

A

x = +|- a/e

21
Q

What are the vertices of a standard hyperbola?

A

(+|- a, 0)

22
Q

What are the asymptotes of an hyperbola in standard position?

A

y = (+|- b/a)x

23
Q

What are the foci of a standard hyperbola?

A

(+|- ae, 0)

24
Q

What are the directrices of an hyperbola in standard position?

A

x = +|- a/e

25
Q

What is the value of the eccentricity e of a parabola?

A

e=1

26
Q

What is the equation of a parabola in standard position?

A

y^2=4ax