I have my final exam tomorrow night and I have "preparation test" I was given, so I have been finding like example questions to quiz myself - here are my weakspots that I can quite get, as there are no samples in all of my textbooks that the same "type":
1. State the sum of focal radii for the ellipse with the equation:
I get 2 different answers via this:
, therefore, a=4
, therefore, b=3
, therefore c=5, therefore the foci=5, therefore sum of focal radii=10
OR, according to my book, sum of focal radii=2a, therfore 2(4)=8?
2. State the equation of the directrix for the parabola with the vertex (0,0) and focus (0, -3).
3. Solve for x:
I have NO idea how to approach this one. I have never seen a variable *in* an exponent. A hint or two, please on how to start? (I am probably just mental-blocking, so a push in the right direction will most likely make me go "AHH!")
Thanks for all & any help!
According to this - Mathwords: Ellipse , your book is right... Anyway its a well know property of an ellipse and in many cases this property is used to distinguish an ellipse from other conics.
[IMG]file:///C:/DOCUME%7E1/THEONE%7E1/LOCALS%7E1/Temp/moz-screenshot.jpg[/IMG][IMG]file:///C:/DOCUME%7E1/THEONE%7E1/LOCALS%7E1/Temp/moz-screenshot-1.jpg[/IMG]First of all since the focus is on the x axis and the vertex is the origin... its a vertical parabola opening downwards. So the equation is of the form2. State the equation of the directrix for the parabola with the vertex (0,0) and focus (0, -3).
, where p is the distance of the vertex from the focus. Here p = 3. Hence the equation is
So you are right(except for a typo)
Thanks for all & any help![/quote]