JEE MATHEMATICS MCQ: TRANSFORMATION OF AXES

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Analyzing +4 | -1

If by rotating the coordinate axes without translating the origin, the expression

a_1 x^2+2 h_1 x y+b_1 y^2

becomes

a_2 X^2+2 h_2 X Y+b_2 Y^2

, then

View answer and explanation

Correct option: A

\left(a_1-b_1\right)^2+4 h_1^2=\left(a_2-b_2\right)^2+4 h_2^2

Option A

\left((a_1 - b_1)^2 + 4h_1^2 = (a_2 - b_2)^2 + 4h_2^2\right)

is correct because it represents an invariant under rotation of coordinate axes.

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