find the equation

**lance** · February 22nd 2010, 10:30 PM

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!

**Soroban** · February 23rd 2010, 02:19 PM

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: . $x^2 \,=\,4py\,\text{ or }\,y^2\,=\,4px$

From [2], the parabola is "horizontal": . $\supset\text{ or } \subset$
. . The equation is of the form: . $y^2 \:=\:4px$ .(a)

From [3], the length of the latus rectum is 5.
We are expected to know that the length of the latus rectum is $4p.$
. . Hence: . $4p = 5$

Substitute into (a): . $y^2 \:=\:5x$

But the parabola can open to the left or the right.

. . Therefore: . $y^2 \;=\;\pm5x$

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