Question

Find an equation for the parabola which fits the given criteria, the endpoints of latus rectum are (2,9) and (6,9)

Answer 1

The equation of parabola is ( x - 4 )² = 4 ( y - 10)

Explanation:

Given as :

The end points latus rectum is ( 2 , 9 ) and ( 6 , 9 )

The equation of parabola is

( x - h )² = 4p ( y - k)

Where ( h , k ) is vertex

And 4p =
`\sqrt{(x_2 - x_1)^(2) + (y_2 - y_1)^(2)}`

Or, 4p =
`\sqrt{(6 - 2)^(2) + (9 - 9)^(2)}`

∴ p = 1

∵ focus is mid point of latus rectum

so ,
`(2+6)/(2)` ,
`(9+9)/(2)`

or focus = ( 4 , 9)

So, vertex (h , k) = ( 4 , 9-1 ) = ( 4 , 8 )

SO, equation is

( x - 4 )² = 4×1 ( y - 8)

Or, ( x - 4 )² = 4 ( y - 8 )

Hence The equation of parabola is ( x - 4 )² = 4 ( y - 8 ) Answer