Hi

Can someone please help me with the following problem?

Find the points of the ellipse 4x^{2 }+ 9y^{2 }=36 that are closest to the point (1,1), as well as the point or points farthest from it?

I have done so far:

g(x,y)=4x^{2 }+ 9y^{2 }- 36 = 0 ==> g_{x}(x,y)=8x & g_{y}(x,y)=18y

The distance from the point is d=sqrt[(x-1)^{2 }+ (y-1)^{2 }]

==> f(x,y)= (x-1)^{2 }+ (y-1)^{2}

==> f_{x}(x,y)=λ.g_{x}(x,y) and f_{y}(x,y)=λ.g_{y}(x,y)

so 2(x-1) = λ . 8x and 2(y-1) = λ . 18y and from above 4x^{2 }+ 9y^{2 }- 36 = 0

How do I solve this?