Find out the coordinates of the extremities of the latus of the parabola x²+y²-16x-16y+2xy+32=0.

Hi Student
x² + y² +2xy -16x + 16y +32= 0
(x+y)² = 16 (x-y -2)
Put Y= x+y
and X= x-y -2
Y²= 16X
Which is required parabola
Y=0 and X=0
will give vertex of parabola
And the axis is given by Y=0
so accordingly you can find focus and from focus you can find cordinates of ends of latus rectum


If you still have problem then reply on this thread.