Mathematics · Coordinate Geometry
The coordinate axes are rotated through an angle of π4 in the anticlockwise direction without shifting the origin. If the equation x2 + y2 - 2x - 4y - 20 = 0 transforms to ax2 + 2hxy + by2 + 2g'x + 2f'y + c' = 0 in the new coordinate system, then what is the value of the determinant Δ = ? Note: For a general second-degree equation, the determinant representing the invariant expression abc + 2hgf - af2 - bg2 - ch2 is invariant under rotation of axes.
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