Flashcards
Ellipses, Parabola, Hyperbola
Cards in this deck (17)
- 1Why are these called conics?As if we cut up a cone at various different angles, we get these different shapes : circles, ellipses, parabola and hyperbola
- 2What is the equation for an ellipse?(x/a)^2 + (y/b)^2 = 1
- 3The ellipse would cross the coordinate axes at....(a,0) , (-a,0) , (0,b) , (0,-b)
- 4If a=b, that means....The ellipse is also a circle
- 5Find the coordinates where 2x^2 + 3y^2=15 crosses the coordinate axesWe need to get into form (x/a)^2+(y/b)^2=1
So: 2x^2 /15 + 3y^2 /15 =1
x^2/(15/2) + y^2/5 = 1
(x/root(15/2))^2 + (y/root(5))^2 = 1
So points: (root(15/2) ,0) , (-root(15/2) ,0)
(0,root(5)) , (0,-root(5)) - 6What is the equation of a parabola?y^2 = 4ax
- 7Why is the equation like this?Essentially, length of line from directrix to (x,y) = a+x , and length of line from focus to (x,y) = root(x-a)^2+y^2 , and if we set these equal then it cancels to y^2=4ax
(dont necessarily need to know this) - 8Equation of rectangular hyperbola:xy=c^2
- 9xy=c^2 has 2 asymptotes. Where are they?x=0 , y=0
- 10xy=c^2 has 2 vertices. Where are they?(c,c) and (-c,-c)
(e.g. xy=9 has vertices (3,3) and (-3,-3) - 11The equation for a Hyperbola is....(x/a)^2 - (y/b)^2 = 1
- 12(x/a)^2 - (y/b)^2 = 1 has asymptotes at....y=b/ax and y=-b/ax
- 13(x/a)^2 - (y/b)^2 = 1 has vertices at....(a,0) and (-a,0)
- 14Diagram of Ellipse:s
- 15Diagram of Parabola y^2=4ax
- 16Diagram of Rectangular Hyperbola
- 17Diagram of Hyperbola
