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Get some graph paper, draw two axes and bisect them with a 45 degree sloping line. Next pick any point on that 45 degree sloping line and from that point draw a line parallel to the horizontal axis so that it intersects the vertical axis. Do the same thing from the point drawing a line parallel with the vertical axis so that it intersects the horizontal axis. These two lines represent represent the components of your vector and if you measure them they will be of equal length and thus of equal magnitude. For ANY angle of slope (other than 45 degrees) the two vectors will not be of equal length.
x2/82 + y2/242 = 1
By taking a coordinate system with origin at the center of the ellipse, and x-axis along the major axis, and y-axis along the minor axis, then the ellipse intercepts the x-axis at -5 and 5, and the y-axis at -2 and 2. So that the equation of the ellipse x2/a2 + y2/b2 = 1 becomes x2/52 + y2/22 = 1 or x2/25 + y2/4 = 1.
An oval, or more technically an ellipse, has a long ( major) axis and short (minor axis). If major axis length is a and minor length is b, then area, A is A = pi*a*b /4 where and so the area of half an oval is pi*a*b/8
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I suggest that the answer is that the statement is false.
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