IGNOU PHE 14 2026 - Identify the conic section whose equation is

Question

Identify the conic section whose equation is

$$5x^2 - 4xy + 5y^2 = 4$

29 Jan 2026

Answer :

Word Count : 370

We are given the equation: [ 5x^2 - 4xy + 5y^2 = 4 ] To identify the conic section, we can use the discriminant method. For a general second-degree equation: [ Ax^2 + Bxy + Cy^2 + Dx + Ey + F = 0 ] the discriminant is: [ \Delta = B^2 - 4AC ] Here, (A = 5), (B = -4), (C = 5). Then, [ \Delta = (-4)^2 - 4(5)(5) = 16 - 100 = -84 ] Since (\Delta < 0) and (A = C > 0), the equation represents an ellipse (specifically, a rotated ellipse because (B \neq 0)). To find

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