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

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

Step-by-step 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 =

Or,  4p =  

∴    p = 1

∵  focus is mid point of latus rectum

so , ,

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

step-by-step explanation:

you can add the two numbers and divide the result by 2. or you can find the gap between the two numbers and add half of this to the smaller number.