Question

Parametric Question (need urgent help)

Answer 1

which part are u stuck at ?

Answer 2

the whole question..

Answer 3

whats the definition of latus rectum ?

Answer 4

a straight horizontal line passing through the focal point?

Answer 5

exactly !
lets convert the given parameteric equation into cartesian form

Answer 6

\[x = 2at\]
\[y = at^2\]

Answer 7

can you eliminate \(t\) ?

Answer 8

so after making t the subject and subbing it into y=at^2 i had \[x^2 = 4ay\]

Answer 9

yes ! a better form would be :
\[\large y = \dfrac{1}{4a}x^2\]

focus = \(\large (0, a)\)

Answer 10

so the equation of line passing through focus would be :
\[\large y = a\]

Answer 11

solve this with the parametric equation to find the intersecting points L and R :

\(y = a\)
\(y = at^2\)

\(t = ?\)

Answer 12

\[a = at^2\]
\[t^2=1\]
\[t= \pm 1\]