What is the foci y^2=1-49x^2 ?

The foci y^2=1-49x^2 is (0,(4sqrt(3))/7),(0,-(4sqrt(3))/7)

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foci y^2=1-49x^2

foci

y^{2} = 1 - 49 x^{2}

(0, \frac{4 3}{7}), (0, - \frac{4 3}{7})

Solution steps

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

Calculate ellipse properties

y^{2} = 1 - 49 x^{2} :

Ellipse with center

(h, k) = (0, 0), b = 1, a = \frac{1}{7}

(0, 0 + c), (0, 0 - c)

Compute

c :

c = 1^{2} - (\frac{1}{7})^{2} : \frac{4 3}{7}

(0, 0 + \frac{4 3}{7}), (0, 0 - \frac{4 3}{7})

Refine

(0, \frac{4 3}{7}), (0, - \frac{4 3}{7})

\frac{( x + 4 ) ^{2}}{9} + \frac{( y - 2 ) ^{2}}{4} = 1

9 x^{2} + 49 y^{2} + 18 x + 294 y - 9 = 0

9 x^{2} + 7 y^{2} - 63 = 0

16 x^{2} + 64 y^{2} = 128

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

What is the foci y^2=1-49x^2 ?
The foci y^2=1-49x^2 is (0,(4sqrt(3))/7),(0,-(4sqrt(3))/7)