4 items are filed under this topic.








The parabola with vertex (7,2) and directrix y = 3 
20090121 

From Deann: Find an equation of the parabola with vetrex (7,2) and directrix y =(3) Answered by Penny Nom. 





The equation of an ellipse 
20050717 

From Allan: I working on a problem that asks me to give the equation of an ellipse when only the location of the directrix and the length of the latus rectum are given. No other points on the ellipse are given. Again, the only "givens" are:
Length of latus rectum = 12
Location of directrix is x = 16
If I could determine the eccentricity, I could proceed from there by taking the ratio of the distance from a focus to the latus rectum point to the distance of the point from the directrix, but I lack the x coordinate of c. I've searched the text, and feel I've "missed something" somewhere! I note that the latus rectum segment is unique in one respect in that it is parallel to the directrix, where any other line segment on the ellipse to the focus would not be. Please indicate where I'm going wrong. Answered by Chris Fisher. 





Parabolas 
19980724 

From Danica: how do you find the focus, vertex, and directrix of 4xy^22y33=0 Answered by Penny Nom. 





Parabolic Mirrors 
19970128 

From Megan Wennberg: Consider a ray of light that passes through a chord of a parabola (the chord is above the focus and parallel to the directrix), hits the parabola at a point (x,y) and is reflected through the focus. If d1 is the distance from the chord to the point of incidence (x,y) and d2 is the distance from (x,y) to the focus, can you prove that the sum of the distances d1+d2 is constant, independent of the particular point of incidence. Answered by Penny Nom. 


