Answer:
x2=−8(y−2)
Step-by-step explanation:
Parabola is a locus of a point which moves at the same distance from a fixed point called the focus and a given line called the directrix.
Let P(x,y) be the moving point on the parabola with
focus at S(h,k)= S(0,0)
& directrix at y= 4
Now,
|PS| = √(x-h)2 + (y-k)2
|PS| = √(x-0)2 + (y-0)2
|PS| = √ x2 + y2
Let ‘d’ be the distance of the moving point P(x,y) to directrix y- 4=0
- d= |ax +by + c|/ √a2 + b2
- d= |y-4|/ √0 + 1
- d= |y-4| units.
equation of parabola is:
- |PS| = d
- √ x2 + y2 = |y-4|
Squaring on both sides, we get:
- x2 + y2 = (y-4)2
- x2 + y2 = y2 -8y + 16
- x2 = - 8y + 16
- x2 = -8 ( y - 2)
This is the required equation of the parabola with focus at (0,0) and directrix at y= 4.
