What is 5x^2+4y^2=56 ?

The solution to 5x^2+4y^2=56 is Ellipse with (h,k)=(0,0),a=(2sqrt(14))/(sqrt(5)),b=sqrt(14)

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5x^2+4y^2=56

5 x^{2} + 4 y^{2} = 56

(h, k) = (0, 0), a = \frac{2 14}{5}, b = 14

Solution steps

5 x^{2} + 4 y^{2} = 56

Rewrite

5 x^{2} + 4 y^{2} = 56

in the form of the standard ellipse equation

\frac{( x - 0 ) ^{2}}{( \frac{2 14}{5} ) ^{2}} + \frac{( y - 0 ) ^{2}}{( 14 ) ^{2}} = 1

Therefore ellipse properties are:

(h, k) = (0, 0), a = \frac{2 14}{5}, b = 14

b > a

therefore

b

is semi-major axis and

a

is semi-minor axis

Ellipse with center (h, k) = (0, 0), b = 14, a = \frac{2 14}{5}

25 x^{2} + 9 y^{2} - 100 y + 18 x - 116 = 0

2 x^{2} + 3 y^{2} + 4 x - 5 y - 6 = 0

2 y - x^{2} - y^{2} > 0

0 = 9 - x^{2} - 9 y^{2}

25 x^{2} + 36 y^{2} = 900

What is 5x^2+4y^2=56 ?
The solution to 5x^2+4y^2=56 is Ellipse with (h,k)=(0,0),a=(2sqrt(14))/(sqrt(5)),b=sqrt(14)