Given 3x2 + 2Y2 = 9x, find the maximum value of x2 + Y2 3x2 means 3x square, and so on Urgent, Can we use the monotonicity and the maximum (minimum) value of the function of higher one to answer?

Given 3x2 + 2Y2 = 9x, find the maximum value of x2 + Y2 3x2 means 3x square, and so on Urgent, Can we use the monotonicity and the maximum (minimum) value of the function of higher one to answer?

3x2+2y2=9x
3x^2-9x+2y^2=0
3(x-3/2)^2+2y^2=27/4
(x-3 / 2) ^ 2 / (9 / 4) + y ^ 2 / (27 / 8) = 1 (elliptic equation)
Let x = 3 / 2 + 3 / 2cosa, y = (3 / 4) √ 6sina, a ∈ [0,2 π)
x2+y2=(3/2+3/2cosa)^2+[(3/4)√6sina]^2
=9/4+9/2cosa+9/4(cosa)^2+27/8(sina)^2
=-9/8(cosa)^2+9/2cosa+45/8
=-9/8(cosa-2)^2+81/8
When cosa = 1, the maximum value of x2 + Y2 is 9 (x = 3, y = 0)
Can we use the monotonicity and the maximum (minimum) value of the function of higher one to answer?
What should be done is as follows:
3x2+2y2=9x,
y^2=-3/2x^2+9/2x
x2+y2=x^2-3/2x^2+9/2x
= -1/2x^2+9/2x
(later, the range of X must be required)