What are it's line of symmetry?
4x^2+y^2=9
my answer is
it has 2 lines of symmetry, the x and y axis
You are correct,
you are looking at an ellipse with centre (0,0)
To determine the lines of symmetry for the equation 4x^2 + y^2 = 9, we can start by rearranging the equation into a more familiar form. Let's isolate the x and y terms:
4x^2 + y^2 = 9
Divide both sides by 9:
(4x^2)/9 + (y^2)/9 = 1
Now, we can rewrite the equation using the variables a^2 and b^2, which will reveal the standard equation for an ellipse:
(x/a)^2 + (y/b)^2 = 1
Comparing this equation to our rearranged equation, we can determine the values of a and b:
a = √(9/4)
b = √(9)
Now, we can identify the lines of symmetry. For an ellipse, the lines of symmetry are the x and y axes. In this case, since a > b, the major axis of the ellipse coincides with the x-axis, while the minor axis aligns with the y-axis.
Therefore, the equation 4x^2 + y^2 = 9 has the x-axis and y-axis as its lines of symmetry.