What is the foci 4x^2+25y^2-40x+150y+225=0 ?

The foci 4x^2+25y^2-40x+150y+225=0 is (5+sqrt(21),-3),(5-sqrt(21),-3)

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foci 4x^2+25y^2-40x+150y+225=0

foci

4 x^{2} + 25 y^{2} - 40 x + 150 y + 225 = 0

(5 + 21, - 3), (5 - 21, - 3)

Solution steps

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

Calculate ellipse properties

4 x^{2} + 25 y^{2} - 40 x + 150 y + 225 = 0 :

Ellipse with center

(h, k) = (5, - 3), a = 5, b = 2

(5 + c, - 3), (5 - c, - 3)

Compute

c :

c = 5^{2} - 2^{2} : 21

(5 + 21, - 3), (5 - 21, - 3)

\frac{( x - 8 ) ^{2}}{64} + \frac{( y - 5 ) ^{2}}{5 ^{2}} = 1

2 x^{2} + 2 y^{2} - 28 x + 12 y + 114 = 0

25 x^{2} + 64 y^{2} = 1600

\frac{( x + 2 ) ^{2}}{22} + \frac{( y + 3 ) ^{2}}{18} = 1

25 (x + 2)^{2} + 4 (y - 3)^{2} = 100

What is the foci 4x^2+25y^2-40x+150y+225=0 ?
The foci 4x^2+25y^2-40x+150y+225=0 is (5+sqrt(21),-3),(5-sqrt(21),-3)