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: .$\displaystyle x^2 \,=\,4py\,\text{ or }\,y^2\,=\,4px$
From [2], the parabola is "horizontal": .$\displaystyle \supset\text{ or } \subset$
. . The equation is of the form: .$\displaystyle y^2 \:=\:4px$ .(a)
From [3], the length of the latus rectum is 5.
We are expected to know that the length of the latus rectum is $\displaystyle 4p.$
. . Hence: .$\displaystyle 4p = 5$
Substitute into (a): .$\displaystyle y^2 \:=\:5x$
But the parabola can open to the left or the right.
. . Therefore: .$\displaystyle y^2 \;=\;\pm5x$