What is the vertices 12x^2+20y^2-12x+40y-37=0 ?

The vertices 12x^2+20y^2-12x+40y-37=0 is ((1+2sqrt(5))/2 ,-1),((1-2sqrt(5))/2 ,-1)

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vertices 12x^2+20y^2-12x+40y-37=0

vertices

12 x^{2} + 20 y^{2} - 12 x + 40 y - 37 = 0

(\frac{1 + 2 5}{2}, - 1), (\frac{1 - 2 5}{2}, - 1)

Solution steps

(h + a, k), (h - a, k)

Calculate ellipse properties

12 x^{2} + 20 y^{2} - 12 x + 40 y - 37 = 0 :

Ellipse with center

(h, k) = (\frac{1}{2}, - 1), a = 5, b = 3

(\frac{1}{2} + 5, - 1), (\frac{1}{2} - 5, - 1)

Refine

(\frac{1 + 2 5}{2}, - 1), (\frac{1 - 2 5}{2}, - 1)

\frac{( x - 5 ) ^{2}}{25} + \frac{( y + 7 ) ^{2}}{16} = 1

(\frac{x ^{2}}{15}) + (\frac{y ^{2}}{16}) = 1

9 x^{2} - 36 x + 4 y^{2} = 0

x^{2} + 4 y^{2} = 4

\frac{( x + 5 ) ^{2}}{9} + (y - 1)^{2} = 1

What is the vertices 12x^2+20y^2-12x+40y-37=0 ?
The vertices 12x^2+20y^2-12x+40y-37=0 is ((1+2sqrt(5))/2 ,-1),((1-2sqrt(5))/2 ,-1)