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Prove that [1/(x+y-a)]+[1/(x-y+a)]+[1/(y-x+a)]=0 represents a parabola

Prove that [1/(x+y-a)]+[1/(x-y+a)]+[1/(y-x+a)]=0 represents a parabola

Grade:12th pass

1 Answers

Saurabh Koranglekar
askIITians Faculty 10341 Points
one year ago
The general form of the equation of Parabola

Ax^2+ Bxy + Cy^2+ Dx + Ey + F = 0

The expression B2- 4AC is the discriminant that is used to determine the type of conic section represented by the equation.

If the equation fulfills these conditions, then it is the parabola.

B^2- 4AC = 0

The form can be obtained as follows


given that
(1/m)+(1/n)+(1/p)=0

simplified form is

mn+mp+np=0

using the conditions and simplification we can prove the needful

Regards

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