अक्षों को मूल बिंदु के परितः वामावर्त (counter-clockwise) दिशा में एक निश्चित कोण से घुमाने पर, यदि समीकरण x2 + 4xy + y2 = 1 बदलकर X2a2 - Y2b2 = 1 हो जाता है, तो √(a2 + b2)a2 का मान है:

By shifting the origin to the point (2, 3) through translation of axes, if the equation of the curve x2 + 3xy - 2y2 + 4x - y - 20 = 0 is transformed to the form Ax2 + Bxy + Cy2 + Dx + Ey + F = 0, then D + E + F =

If the transformed equation of the equation 2x2 + 3xy - 2y2 - 17x + 6y + 8 = 0 after translating the coordinate axes to a new origin (α, β) is aX2 + 2hXY + bY2 + c = 0, then the value of 3α + c is: