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

Answer:

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 = $\sqrt{(x_2 - x_1)^{2} + (y_2 - y_1)^{2}}$

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

∴    p = 1

∵  focus is mid point of latus rectum

so , $\frac{2+6}{2}$ , $\frac{9+9}{2}$

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