Purpose of rotating the xy-coordinate system?
a million) Subtract h and ok from x and y, respectively. So, P' = (-2-(-a million), 5-2) = (-a million, 3). 2) Given Ax^2 + Bxy + Cy^2 + Dx + Ey + F = 0, locate t by ability of cot(2t) = (A-C)/B. Then, (x, y) = (x' cos t - y' sin t, x' sin t + y' cos t) right here, cot(2t) = (a million-a million)/2 = 0. So, 2t = pi/2 ==> t = pi/4. So, (x, y) = (x' cos pi/4 - y' sin pi/4, x' sin pi/4 + y' cos pi/4) ==> x = x' sqrt(2)/2 - y' sqrt(2)/2 y = x' sqrt(2)/2 + y' sqrt(2)/2 Substituting those into x^2 + 2xy + y^2 + 4sqrt(2) x - 4sqrt(2) y = 0 : [(x')^2/2 - x'y' + (y')^2/2] + [(x')^2 - (y')^2] + [(x')^2/2 + x'y' + (y')^2/2] + [4x' - 4y'] - [4x' + 4y'] = 0 ==> 2(x')^2 - 8y' = 0 ==> y' = (x')^2 / 4, determination A).