Pure Mathematics - Conic Sections Flashcards
1
Q
What are the 4 conic sections
A
- Circles
- Parabola
- Ellipse
- Hyperbola
2
Q
What is the general equation for an ellipse
A
(x^2 / a^2) + (y^2 / b^2) = 1
3
Q
what is the general equation for a hyperbola
A
(x^2 / a^2) - (y^2 / b^2) = 1
4
Q
What is the general equation for a parabola
A
y^s = 4ax
5
Q
How do you find the vertices of a hyperbola
A
You can find the x-intercepts, which are also the vertices of the curve , by setting y = 0.
6
Q
How do you find the equation of the asymptotes of a hyperbola
A
y = +- (b/a) x
7
Q
What is the transformation of f(x-p) and g(y-q)
A
Translation by vector pi+qj
8
Q
What is the transformation of f(x/p) and g(y/q)
A
- Horizontal stretch by scale factor p
- Vertical stretch by scale factor q
9
Q
What are the 4 reflection transformations
A
- Replacing x with -x reflects a curve in the y-axis
- Replacing y with -y reflects a curve in the x-axis
- Replacing x with y reflects a curve in the line y = x
- Replacing x with -y and y with -x reflects a curve in the line y = -x
