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Question

The transformed equation of 3x2+3y2+2xy=2 when the coordinate axes are rotated through an angle of 450 is

A
X2+2Y2=1
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B
2X2+Y2=1
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C
X2+Y2=1
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D
X2+3Y2=1
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Solution

The correct option is B 2X2+Y2=1

When axes are rotated through 450 ,

x=xcosθysinθ=xy2

y=xsinθycosθ=x+y2

3x2+3y2+2xy=23(xy2)2+3(x+y2)2+2(x2y22)=2

3(x2+y22xy)+3(x2+y2+2xy)+2x22y2=4

4(2x2+y2)=4

2x2+y2=1


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