What is the foci (x^2)/(9/4)+(y^2)/(25/4)=1 ?

The foci (x^2)/(9/4)+(y^2)/(25/4)=1 is (0,2),(0,-2)

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foci (x^2)/(9/4)+(y^2)/(25/4)=1

foci

\frac{x ^{2}}{\frac{9}{4}} + \frac{y ^{2}}{\frac{25}{4}} = 1

(0, 2), (0, - 2)

Solution steps

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

Calculate ellipse properties

\frac{x ^{2}}{\frac{9}{4}} + \frac{y ^{2}}{\frac{25}{4}} = 1 :

Ellipse with center

(h, k) = (0, 0), b = \frac{5}{2}, a = \frac{3}{2}

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

Compute

c :

c = (\frac{5}{2})^{2} - (\frac{3}{2})^{2} : 2

(0, 0 + 2), (0, 0 - 2)

Refine

(0, 2), (0, - 2)

\frac{( x - 3 ) ^{2}}{25} + \frac{( y - 3 ) ^{2}}{4} = 1

\frac{( x - 3 ) ^{2}}{25} + \frac{( y + 3 ) ^{2}}{4} = 1

\frac{( x - 8 ) ^{2}}{2} + \frac{( y - 3 ) ^{2}}{27} = 1

x^{2} + 4 y^{2} + 6 x + 16 y + 21 = 0

3 x^{2} + y^{2} = 6

What is the foci (x^2)/(9/4)+(y^2)/(25/4)=1 ?
The foci (x^2)/(9/4)+(y^2)/(25/4)=1 is (0,2),(0,-2)