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Q.

The transformed equation of 17x2−16xy+17y2=225 when the axes are rotated through an angle of 450 is 9X2 +25Y2 = a2 then a =

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answer is 15.

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Detailed Solution

Put θ=45∘ in  x=Xcos⁡θ−Ysin⁡θ and 
y=Xsin⁡θ+Ycos⁡θ⇒x=X−Y2,y=X+Y2

Transformed equation is 9X2+25Y2=225

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The transformed equation of 17x2−16xy+17y2=225 when the axes are rotated through an angle of 450 is 9X2 +25Y2 = a2 then a =