The transformed equation of $17 x^{2} - 16 x y + 17 y^{2} = 225$ when the axes are rotated through an angle of 45⁰ is 9X² +25Y² = a² then a =

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Detailed Solution

Put $θ = 45^{\circ} in x = X \cos θ - Y \sin θ$ and
$\begin{matrix} y = X \sin θ + Y \cos θ \\ \Rightarrow x = \frac{X - Y}{\sqrt{2}}, y = \frac{X + Y}{\sqrt{2}} \end{matrix}$

Transformed equation is $9 X^{2} + 25 Y^{2} = 225$

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