Question

Find the coordinate of focus equation of directrix langth of latus Rectum and coordinate of end front of latus Rectum for the parabola.
$5x^2=8y$

Answer 1

comparing equation with standard equation $x^2$=4ay

a=2/5

co-ordinates of focus =(o,a) i.e. (0, 2/5)

equation of directrix=y=-a i.e. y=-(2/5)

length of latus rectum= 4a i.e. 8/5

co-ordinates of latus rectum=(-2a,a) and (2a,a) i.e. (-4/5,2/5) and (4/5,2/5)