The transformed equation of $x^2+6xy+8y^2=10$ when the axes are rotated through an angle $\large\frac{\pi}{4}$ is :

Question

\[\begin {array} {1 1} (a)\;15x^2-14xy+3y^2=20 & \quad (b)\;15x^2+14xy-3y^2=20 \\ (c)\;15^2+14xy+3y^2=20 & \quad (d)\;15x^2-14xy-3y^2=20 \end {array}\]