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!

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- Feb 22nd 2010, 10:30 PMlancefind the equation
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! - Feb 23rd 2010, 02:19 PMSoroban
Hello, lance!

Quote:

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 leftthe right.*or*

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