Question

When the origin is shifted to the point (2, 3), the transformed equation of a curve is
x² + 3xy - 2y² + 17x – 7y – 11 = 0. Find the original equation of the curve

Answer 1

Answer:Given when the origin is shifted to the point (2,3)the transformed equation of a curve is x²+3xy-2y²+17x-7y-11 = 0.find the original equation of the curve

Given transformed equation will be

           X^2 + 3XY – 2Y^2 + 17 X – 7Y – 11 = 0

       X = x – h  and Y = y – k

Given new origin = (2,3)

             So we get

              X = x – 2 and Y = y – 3

  Substituting X and Y we get

    (x – 2)^2 + 3 (x – 2) (y – 3) – 2 (y – 3)^2 + 17 (x – 2) – 7(y – 3) – 11 = 0 x^2 + 4 – 4x + 3(xy – 2y – 3x + 6) – 2(y^2 + 9 – 6y) + 17x – 34 – 7y + 21 – 11 = 0

x^2 + 4 – 4x + 3xy – 6y – 9x + 18 – 2y^2 – 18 + 12y + 17x – 34 – 7y + 21 – 11 = 0

x^2 + 3xy – 2y^2 + 4x – y – 20 = 0 will be the original equation. of curve.

Step-by-step explanation:

Answer 2

Answer:

Given when the origin is shifted to the point (2,3)the transformed equation of a curve is x²+3xy-2y²+17x-7y-11 = 0.find the original equation of the curve

Given transformed equation will be

           X^2 + 3XY – 2Y^2 + 17 X – 7Y – 11 = 0

       X = x – h  and Y = y – k

Given new origin = (2,3)

             So we get

              X = x – 2 and Y = y – 3

  Substituting X and Y we get

    (x – 2)^2 + 3 (x – 2) (y – 3) – 2 (y – 3)^2 + 17 (x – 2) – 7(y – 3) – 11 = 0 x^2 + 4 – 4x + 3(xy – 2y – 3x + 6) – 2(y^2 + 9 – 6y) + 17x – 34 – 7y + 21 – 11 = 0

x^2 + 4 – 4x + 3xy – 6y – 9x + 18 – 2y^2 – 18 + 12y + 17x – 34 – 7y + 21 – 11 = 0

x^2 + 3xy – 2y^2 + 4x – y – 20 = 0 will be the original equation. of curve.

Step-by-step explanation: