Find the equation of the parabola with focus (-4,0) and directrix x=4. What is the length of its latus rectum?

Question

Find the equation of the parabola with focus (-4,0) and directrix x=4. What is the length of its latus rectum?

Answer 1

 

Hi Billy,

 

According to the definition of a parabola,

 

any point, (x, y), on the parabola needs to satisfy the following equation.

 

     √((x - (-4))² + (y - 0)²) = |x - 4|     (Eq. 1)

 

By squaring both sides of Eq. 1, we get

 

     (x+4)² + y² = (x-4)²     (Eq. 2)

 

By simplifying Eq. 2, we get the equation of the parabola

 

     x = -(1/16)y²     (Eq. 3)

 

The length of latus rectum,

 

which is 4 times the distance from the focus (-4, 0) to the vertex (0, 0),

 

is given by

 

     4 × |-4 - 0| = 16

 

Hope these help.