What is the foci (25x^2)/4-50x+100y^2+800y+1075=0 ?

The foci (25x^2)/4-50x+100y^2+800y+1075=0 is ((8+5sqrt(15))/2 ,-4),((8-5sqrt(15))/2 ,-4)

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foci (25x^2)/4-50x+100y^2+800y+1075=0

foci

\frac{25 x ^{2}}{4} - 50 x + 100 y^{2} + 800 y + 1075 = 0

(\frac{8 + 5 15}{2}, - 4), (\frac{8 - 5 15}{2}, - 4)

Solution steps

(h + c, k), (h - c, k)

Calculate ellipse properties

\frac{25 x ^{2}}{4} - 50 x + 100 y^{2} + 800 y + 1075 = 0 :

Ellipse with center

(h, k) = (4, - 4), a = 10, b = \frac{5}{2}

(4 + c, - 4), (4 - c, - 4)

Compute

c :

c = 1 0^{2} - (\frac{5}{2})^{2} : \frac{5 15}{2}

(4 + \frac{5 15}{2}, - 4), (4 - \frac{5 15}{2}, - 4)

Refine

(\frac{8 + 5 15}{2}, - 4), (\frac{8 - 5 15}{2}, - 4)

5 x^{2} + y^{2} = 5

8 x^{2} + 9 y^{2} - 72 = 0

\frac{y ^{2}}{169} + \frac{x ^{2}}{25} = 1

\frac{( x - 3 ) ^{2}}{16} + \frac{( y - 2 ) ^{2}}{9} = 1

x^{2} + 4 x + 4 y^{2} = 0

What is the foci (25x^2)/4-50x+100y^2+800y+1075=0 ?
The foci (25x^2)/4-50x+100y^2+800y+1075=0 is ((8+5sqrt(15))/2 ,-4),((8-5sqrt(15))/2 ,-4)