Question

find the co-ordinate of the focus ,equation of the directrix length of latus rectum of parabola,i)5y²=24x. ii)x²=12y iii)3x²=-16x​

Answer 1

Answer:

1 ) .

Given :

5 y² = 24 x

y² = 4 ( 6 / 5 ) x

We have general equation of parabola i.e.

y² = 4 a x

Comparing this we get :

a = 6 / 5

Co-ordinate of focus ( 6 / 5 , 0 )

Equation of directrix :

x = - 6  / 5

5 x + 6 = 0

Length of latus rectum :

L = 2 × 6 / 5

L = 12 / 5

2 ) .

x² = 12 y

x² = 4 ( 3 ) y

We have :

x² = 4 a y

a = 3

Co-ordinate of focus ( 0 , 3 )

Equation of directrix :

y = - 3

y + 3 = 0

Length of latus rectum :

L = 2 * 3

L = 6

3 ) .

3 x² = - 16 x

x² = 4 ( - 4 / 3 ) x

We get :

a = - 4 / 3

Co-ordinate of focus ( 0 , 4 / 3 )

Equation of directrix :

y = a

y = - 4 / 3

3 y + 4 = 0

Length of latus rectum :

L = 2 a

L = 8 / 3.