What is x^2+5y^2=9(2.1) ?

The solution to x^2+5y^2=9(2.1) is Ellipse with (h,k)=(0,0),a=4.34741…,b=1.94422…

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x^2+5y^2=9(2.1)

x^{2} + 5 y^{2} = 9 (2.1)

(h, k) = (0, 0), a = 4.34741 \dots, b = 1.94422 \dots

Solution steps

x^{2} + 5 y^{2} = 9 \cdot 2.1

Rewrite

x^{2} + 5 y^{2} = 92.1

in the form of the standard ellipse equation

\frac{( x - 0 ) ^{2}}{4.34741 \dots ^{2}} + \frac{( y - 0 ) ^{2}}{1.94422 \dots ^{2}} = 1

Therefore ellipse properties are:

(h, k) = (0, 0), a = 4.34741 \dots, b = 1.94422 \dots

a > b

therefore

a

is semi-major axis and

b

is semi-minor axis

Ellipse with center (h, k) = (0, 0), a = 4.34741 \dots, b = 1.94422 \dots

81 x^{2} + 16 y^{2} = 1296

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

\frac{( x - 4 ) ^{2}}{24} + \frac{( y - 2 ) ^{2}}{49} = 1

5 x^{2} + 2 y^{2} - 10 x + 18 y - 10 = 0

\frac{x ^{2} + y ^{2} - x}{2 x - x ^{2} - y ^{2}} > 0

What is x^2+5y^2=9(2.1) ?
The solution to x^2+5y^2=9(2.1) is Ellipse with (h,k)=(0,0),a=4.34741…,b=1.94422…