What is the vertices 36x^2+9y^2+48x-36y+43=0 ?

The vertices 36x^2+9y^2+48x-36y+43=0 is (-2/3 ,3),(-2/3 ,1)

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vertices 36x^2+9y^2+48x-36y+43=0

vertices

36 x^{2} + 9 y^{2} + 48 x - 36 y + 43 = 0

(- \frac{2}{3}, 3), (- \frac{2}{3}, 1)

Solution steps

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

Calculate ellipse properties

36 x^{2} + 9 y^{2} + 48 x - 36 y + 43 = 0 :

Ellipse with center

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

(- \frac{2}{3}, 2 + 1), (- \frac{2}{3}, 2 - 1)

Refine

(- \frac{2}{3}, 3), (- \frac{2}{3}, 1)

16 x^{2} - 96 x + 4 y^{2} = - 80

x^{2} + 16 y^{2} - 64 = 0

\frac{( x - 7 ) ^{2}}{4} + \frac{( y + 3 ) ^{2}}{16} = 1

\frac{( x + 3 ) ^{2}}{9} + \frac{( y - 1 ) ^{2}}{25} = 1

\frac{x ^{2}}{81} + \frac{y ^{2}}{49} = 1

What is the vertices 36x^2+9y^2+48x-36y+43=0 ?
The vertices 36x^2+9y^2+48x-36y+43=0 is (-2/3 ,3),(-2/3 ,1)