What is 8y^2=-9/2 x^2+25/2 ?

The solution to 8y^2=-9/2 x^2+25/2 is Ellipse with (h,k)=(0,0),a= 5/3 ,b= 5/4

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8y^2=-9/2 x^2+25/2

8 y^{2} = - \frac{9}{2} x^{2} + \frac{25}{2}

(h, k) = (0, 0), a = \frac{5}{3}, b = \frac{5}{4}

Solution steps

8 y^{2} = - \frac{9}{2} x^{2} + \frac{25}{2}

Rewrite

8 y^{2} = - \frac{9}{2} x^{2} + \frac{25}{2}

in the form of the standard ellipse equation

\frac{( x - 0 ) ^{2}}{( \frac{5}{3} ) ^{2}} + \frac{( y - 0 ) ^{2}}{( \frac{5}{4} ) ^{2}} = 1

Therefore ellipse properties are:

(h, k) = (0, 0), a = \frac{5}{3}, b = \frac{5}{4}

a > b

therefore

a

is semi-major axis and

b

is semi-minor axis

Ellipse with center (h, k) = (0, 0), a = \frac{5}{3}, b = \frac{5}{4}

x^{2} + 3 y^{2} = 28

12 x^{2} + 3 y^{2} + 12 y - 96 = 0

\frac{( x - 3 ) ^{2}}{2} + (y + 5)^{2} = 8

(\frac{x - 2}{9})^{2} + (\frac{y + 2}{25})^{2} = 1

25 x^{2} + 64 y^{2} - 400 x - 640 y + 1600 = 0

What is 8y^2=-9/2 x^2+25/2 ?
The solution to 8y^2=-9/2 x^2+25/2 is Ellipse with (h,k)=(0,0),a= 5/3 ,b= 5/4