Conics help needed (1 Viewer)

[Aesytic]

hey all

i've just started 4unit this week and so far we've done some work on ellipses and hyperbolas, but there's this question that i have trouble with:

find the equations of each of the following conics. sketch each curve.
a) focus (3,5), directrix 2x+y-4=0, eccentricity 1/3
b) focus (-1,1), directrix x+y+1=0, eccentricity 4/3
c) focus (2,-1), directrix x-y+1=0, eccentricity 1

the ones where the directrices are either vertical or horizontal i have no trouble with, but these ones put me off...are these conics slanted or something??

thanks in advance

 

[seanieg89]

Yes, these conics are oblique. Use the perpendicular distance formula and the focus-directrix definition of conics to find their equations and sketch them.

 

[Aesytic]

ohh i see, thanks for the help!

i'm still having trouble with sketching them though...not really sure where to start

 

[seanieg89]

Think carefully about the relationship between conics and their focii/directrices. Perhaps it might be easier to start by thinking about how to sketch the parabola with vertex at O and focus at (1,1).

Also, the equations you have hopefully found will give you all information about the conics x & y intercepts.

 

[Sanefo]

Genius, Thanks