Find the equation of the parabola with vertex: (0,0); axis: x axis; length of latus rectum: 5.
Please help me and show the solution... Or just give me an idea on how to answer this question... Thanks!
Hello, lance!
Find the equation of the parabola with:
. . [1] Vertex: (0,0)
. . [2] Axis: x-axis
. . [3] Length of latus rectum: 5
From [1], the vertex is at the Origin.
. . The equation is of the form: .
From [2], the parabola is "horizontal": .
. . The equation is of the form: . .(a)
From [3], the length of the latus rectum is 5.
We are expected to know that the length of the latus rectum is
. . Hence: .
Substitute into (a): .
But the parabola can open to the left or the right.
. . Therefore: .