What is the foci x^2+4y^2-6x+8y-3=0 ?

The foci x^2+4y^2-6x+8y-3=0 is (3+2sqrt(3),-1),(3-2sqrt(3),-1)

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foci x^2+4y^2-6x+8y-3=0

foci

x^{2} + 4 y^{2} - 6 x + 8 y - 3 = 0

(3 + 23, - 1), (3 - 23, - 1)

Solution steps

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

Calculate ellipse properties

x^{2} + 4 y^{2} - 6 x + 8 y - 3 = 0 :

Ellipse with center

(h, k) = (3, - 1), a = 4, b = 2

(3 + c, - 1), (3 - c, - 1)

Compute

c :

c = 4^{2} - 2^{2} : 23

(3 + 23, - 1), (3 - 23, - 1)

\frac{x ^{2}}{36} + \frac{y ^{2}}{121} = 1

2 x^{2} + y^{2} + 12 x - 2 y + 11 = 0

16 x^{2} + 9 y^{2} + 64 x - 80 = 0

\frac{x ^{2}}{4} + \frac{y ^{2}}{1} = 1

16 x^{2} + 4 y^{2} + 96 x - 24 y + 116 = 0

What is the foci x^2+4y^2-6x+8y-3=0 ?
The foci x^2+4y^2-6x+8y-3=0 is (3+2sqrt(3),-1),(3-2sqrt(3),-1)