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 = [tex]\sqrt{(x_2 - x_1)^{2} + (y_2 - y_1)^{2}}[/tex]
Or, 4p = [tex]\sqrt{(6 - 2)^{2} + (9 - 9)^{2}}[/tex]
∴ p = 1
∵ focus is mid point of latus rectum
so , [tex]\frac{2+6}{2}[/tex] , [tex]\frac{9+9}{2}[/tex]
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
