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

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

Grade:12

1 Answers

Harsh Patodia IIT Roorkee
askIITians Faculty 907 Points
9 years ago
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


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