What is the vertices 16y^2+25x^2-80x+36y+80=0 ?

The vertices 16y^2+25x^2-80x+36y+80=0 is (8/5 ,(-9+sqrt(17))/8),(8/5 ,(-9-sqrt(17))/8)

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vertices 16y^2+25x^2-80x+36y+80=0

vertices

16 y^{2} + 25 x^{2} - 80 x + 36 y + 80 = 0

(\frac{8}{5}, \frac{- 9 + 17}{8}), (\frac{8}{5}, \frac{- 9 - 17}{8})

Solution steps

(h, k + b), (h, k - b)

Calculate ellipse properties

16 y^{2} + 25 x^{2} - 80 x + 36 y + 80 = 0 :

Ellipse with center

(h, k) = (\frac{8}{5}, - \frac{9}{8}), b = \frac{17}{8}, a = \frac{17}{10}

(\frac{8}{5}, - \frac{9}{8} + \frac{17}{8}), (\frac{8}{5}, - \frac{9}{8} - \frac{17}{8})

Refine

(\frac{8}{5}, \frac{- 9 + 17}{8}), (\frac{8}{5}, \frac{- 9 - 17}{8})

4 x^{2} + 9 y^{2} - 48 x + 72 y = - 144

\frac{( x - 1 ) ^{2}}{45} + \frac{( y - 2 ) ^{2}}{20} = 1

4 x^{2} + 9 y^{2} - 16 x - 18 y - 11 = 0

x^{2} + 3 y^{2} = 6

x^{2} + 3 y^{2} - 6 x + 6 y = 0

What is the vertices 16y^2+25x^2-80x+36y+80=0 ?
The vertices 16y^2+25x^2-80x+36y+80=0 is (8/5 ,(-9+sqrt(17))/8),(8/5 ,(-9-sqrt(17))/8)