what is the equation of image of the circle "x^2+y^2=4" after applying the "sheer transformation" along "x-axi

Question

what is the equation of image of the circle "x^2+y^2=4" after applying the "sheer transformation" along "x-axis" by factor "2"

Answer 1

Let x', y' denote the x and y-coordinates of the transformed circle. Then:
x'=x+2y
y'=y
So:
y=y'
x=x'-2y'
(x'-2y')²+y'²=4
(x')² +5(y')² - 4x'y' = 4

Answer 2

I don't know what "sheer transformation" is, but if it is linear transformation along the x axis by a factor of 2, then each value of x must be multiplied by 2, so the resulting equation is

(2x)^2 + y^2 = 4, or 4x^2 + y^2 = 4

It is no longer a circle.

Answer 3

for shear w1 = x1 + 2x2 = x + 2y
w2 = x2 = y

so the image of the circle will be:
w1^2 + w2^2 = 4
or, (x+2y)^2 + y^2 = 4
or, x^2 + 4xy + 5y^2 = 4