Question

5. If the transformed equation of a curve is
0) X^2+3XY-2y^2+17x- 7y - 11 = 0 when the axes are translated to the point
(2,3), then find the original equation of the curve
​

Answer 1

Answer:

x² + 3xy - 2y² + 4x - y - 20 = 0

Step-by-step explanation:

New origin = (2, 3) = (h, k)

Equation of transformation are :

x² - 2y² + 3xy + 17x - 17y - 11 = 0

Then,

Original equation will be :

=> (x - 2)² - 2(y - 3)² + 3(x - 2) (y - 3) + 17(x - 2) - 17(y - 3) - 11 = 0

=> x² + 4x + 4 + 3xy - 9x - 6y + 18 - 2y² +12y - 18 + 17x - 34 - 7y + 21 - 11 = 0

=> x² + 3xy - 2y² + 4x - 9x + 17x - 6y - 7y - 20 = 0

=> x² + 3xy - 2y² + 4x - y - 20 = 0

Therefore,

The required original equation is :

x² + 3xy - 2y² + 4x - y - 20 = 0

Hope it helps you sister!

Answer 2

Step-by-step explanation:

refer above information

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