if equation of directrix of a parabola is 2x+3=0, axis is 2y-3=0 and length of latus rectum is 6 then what will be the focus?

Answer 1

Given: 2x + 3 = 0, 2y - 3 = 0, Latus
Rectum = 6.

Eq1: y = 2x + 3.
Eq2: x = 2y - 3.

In Eq1, substitute 2y - 3 for x:
y = 2(2y-3) + 3,
y = 4y - 6 + 3,
y - 4y = -3,
-3y = -3,
y = 1.

In Eq2, substitute 1 for y:
x = 2*1 - 3 = -1.

D(-1,1).

1/a = 6,
a = 1/6.
4a = 4/6 = 2/3.
1/4a = 3/2.

F(-1,y)

V(-1,5/2)

D(-1,1)

k = 1 + 1/4a = 1 + 3/2 = 5/2 = 2 1/2.

y = k + 1/4a = 5/2 + 3/2 = 8/2 = 4.