Locus problem #1

Geometry Level 3

If a parabola whose length of latus rectum is 4 a 4a touches both coordinate axes then the locus of its focus is :

x y = a 2 ( x 2 + y 2 ) xy=a^2(x^2+y^2) x 2 y 2 = a 2 ( x 2 + y 2 ) x^2y^2=a^2(x^2+y^2) x 2 y 2 = a 2 ( x 2 − y 2 ) x^2y^2=a^2(x^2-y^2) x 2 − y 2 = a 2 ( x 2 + y 2 ) x^2-y^2=a^2(x^2+y^2)

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1 solution

Use the fact : 1 p 1 2 + 1 p 2 2 = 1 a 2 \dfrac{1}{p_{1}^2}+\dfrac{1}{p_{2}^2}=\dfrac{1}{a^2} where p 1 p_{1} and p 2 p_{2} are lengths of perpendiculars from focus on two perpendicular tangents .

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