Which of the following statements are correct?
The focus of x2=4ay is (0, a)
The parabolas x2=4ay and y2=4ax are equal.
The coordinates of focus becomes (0,a) from (a,0). Directrix become y+a=0 from x+a=0.
1) Focus of x2=4ay is (0,a)
⇒ True
2)We want to find the directrix of y2=−4ax
We get y2=−4ax by rotating x2=4ay through 90∘ or y2=4ax by 180∘
It is the reflection of y2=4ax about y-axis. so the directrix become x=a from x=−a
⇒ not correct
Latus rectum is the chord passing through focus and perpendicular to axis. Now, the end points of latus rectum is the points where latus rectum meet the parabola. Let us draw it for x2=−4ay
Let p(x, y) be one of the end points we can see that the y-coordinate of P and focus are same.
⇒ y=−a
(x, y) lies on x2=−4ay
⇒x2=−4ax−a=4a2
⇒x=∓2a
So the end points are (2a, -a) and (-2a, -a)
⇒statement 3 is false
4) We say two parabolas are equal if they have same latus rectam.y2=4ax and x2=4ay have the same latus rectum (4a)
⇒ statement 4 is true.
So the statements 1 and 4 are correct.