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Given the equation 4x^2+2sqrt(3)x y+2y^2...

Given the equation `4x^2+2sqrt(3)x y+2y^2=1` . Through what angle should the axes be rotated so that the term `x y` is removed from the transformed equation.

Text Solution

Verified by Experts

The correct Answer is:
`pi//6,2pi//3`
Comparing the given equation with `ax^2+2hxy+by^2`
we get `a=4,h=sqrt3,b=2`.
Let `theta` be the angle through which the axes are to be rotated. Then,
`tan 2theta=(2h)/(a b)`
or `tan2theta=(2sqrt3)/(4-2)=sqrt(3)=tan.(pi)/(3)`
or `2theta=(pi)/(3),pi+(pi)/(3)`
or `theta=(pi)/(6),(2pi)/(3)`
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