Locus Q (1 Viewer)

[Lukybear]

The latus rectum of a parabola has endpoints (-2,3) and (6,3). Find two possible equations for the parabola.

Very difficult for me.

 

[gurmies]

End points are (-2,3) and (6,3)

(-2 + 6)/2 = 2

.'. x = 2 is the axis of symmetry.

Length of latus rectum is 4a units (easily proven)

4a = 6+|-2| = 8

a = 2

y-coordinate of the vertex can be either 3-2 = 1 or 3+2 = 5

(x-2)^2 = 8(y-1) or/ (x-2)^2 = -8(y-5)

 

[Lukybear]

Length of latus rectum is 4a units (easily proven)

Whats the proof?

 

[ninetypercent]

latus rectum has the equation y = a

equation of parabola

x^2 = 4ay

substitute y = a for y

x^2 = 4a^2
x = +/- 2a

therefore, the length of the latus recturm is 2a + 2a = 4a units

 

[Lukybear]

nvm

EDIT: Thanxs anywaz.

 

[mtsmahia]

so the length of the latus rectum for any parabola is 4a right?

 

[jet]

Always. It's a property of the parabola.