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AP EAMCET · Maths · Straight Lines

By shifting the origin to the point \((2,3)\) through translation of axes, if the equation of the curve \(x^2+3 x y-2 y^2+4 x-y-20=0\) is transformed to the form \(\mathrm{Ax}^2+\mathrm{Bxy}+\mathrm{Cy}^2+\mathrm{Dx}+\mathrm{Ey}+\mathrm{F}=0\), then \(\mathrm{D}+\mathrm{E}+\mathrm{F}=\)

  1. A \(-1\)
  2. B \(1\)
  3. C \(-15\)
  4. D \(15\)
Verified Solution

Answer & Solution

Correct Answer

(A) \(-1\)

Step-by-step Solution

Detailed explanation

\( \frac{\partial}{\partial x}(x^2+3xy-2y^2+4x-y-20) = 2x+3y+4 \) \( D = 2(2)+3(3)+4 = 17 \) \( \frac{\partial}{\partial y}(x^2+3xy-2y^2+4x-y-20) = 3x-4y-1 \) \( E = 3(2)-4(3)-1 = -7 \) \( F = (2)^2+3(2)(3)-2(3)^2+4(2)-(3)-20 \) \( F = 4+18-18+8-3-20 = -11 \)…