Question

by a suitable translation of the coordinates axes , remove the term of the first degree in the equation x2 +3xy -y2 +3x-7y+11=0
​

Answer 1

Answer:

thx 4 points

Step-by-step explanation:

its 45

Answer 2

The suitable translation of the coordinates axes is x = x' - 23/13 , y = y' + 15/13

Given :

An equation x² + 3xy - y² + 3x - 7y + 11 = 0

To find :

The suitable translation of the coordinates axes

Solution :

Step 1 of 4 :

Write down the given equation

The given equation is

x² + 3xy - y² + 3x - 7y + 11 = 0

Step 2 of 4 :

Assume the translation of the coordinates axes

Let (x, y) be coordinates of a point in old cartesian coordinate system

Let after translation of origin to (h, k) the point (x, y) is translated to (x', y')

Step 3 of 4 :

Find the system of equations

In order to remove the term of the first degree in the equation we have

Coefficient of x' = 0

⇒ 2h + 3k + 3 = 0 - - - - - (1)

Coefficient of y' = 0

⇒ 3h - 2k - 7 = 0 - - - - - (2)

Step 4 of 4 :

Find the required translation of the coordinates axes

Solving Equation 1 and Equation 2 we get

h = - 23/13 & k = 15/13

Hence the required translation of the coordinates axes is x = x' - 23/13 , y = y' + 15/13

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