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When the coordinate axes are rotated about the origin in the positive direction through an angle $\frac{π}{4},$ if the equation $49 x^{2} + 25 y^{2} = 1225$ is transformed to $p x^{2} + q x y + r y^{2} = t$ and the GCD of p, q, r, t is 1, then

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${(p - q + r - 32)}^{2} = 4 t$

${(p - q - r + 12)}^{2} = t$

${(p + q + r - 15)}^{2} = t$

${(- p - q + r + 13)}^{2} = t$

answer is C.

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Use rotation formulae

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