Question

. If the axes are translated to the point (-2,-3) then the equation
x2+3y2 +4x+18y+30=0 transforms to​

Answer 1

Transformation of co-ordinates

Given: the axes are translated to the point (- 2, - 3)

To find: the transformed equation of x² + 3y² + 4x + 18y + 30 = 0

Solution:

The transformation formulæ are

• x = x' - 2 and y = y' - 3

Then the given equation becomes

(x' - 2)² + 3 (y' - 3)² + 4 (x' - 2) + 18 (y' - 3) + 30 = 0

or, x'² - 4x' + 4 + 3y'² - 18y' + 27 + 4x' - 8 + 18y' - 54 + 30 = 0

or, x'² + 3y'² = 1

This equation can be written as,

x² + 3y² = 1

which is the required transomed equation.

Answer 2

Given :- origin :- (-2,-3)

therefore, h= -2 & k= -3..

we know, x=x'-2

& y=y'-3

put x nd y value in equation,

answer :---

x' ^ 2 + 3y' ^ 2 -1 =0

hope it will help u all...