What is 0.11x^2+0.25y^2=1 ?

The solution to 0.11x^2+0.25y^2=1 is Ellipse with (h,k)=(0,0),a=3.01511…,b=2

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0.11x^2+0.25y^2=1

0.11 x^{2} + 0.25 y^{2} = 1

(h, k) = (0, 0), a = 3.01511 \dots, b = 2

Solution steps

0.11 x^{2} + 0.25 y^{2} = 1

Rewrite

0.11 x^{2} + 0.25 y^{2} = 1

in the form of the standard ellipse equation

\frac{( x - 0 ) ^{2}}{3.01511 \dots ^{2}} + \frac{( y - 0 ) ^{2}}{2 ^{2}} = 1

Therefore ellipse properties are:

(h, k) = (0, 0), a = 3.01511 \dots, b = 2

a > b

therefore

a

is semi-major axis and

b

is semi-minor axis

Ellipse with center (h, k) = (0, 0), a = 3.01511 \dots, b = 2

2 x^{2} + 3 y^{2} + 4 x = 1

3 x^{2} + 8 y^{2} + 12 x + 48 y + 60 = 0

16 x^{2} + 25 y^{2} + 32 x - 384 = 0

9 x^{2} + 4 y^{2} - 36 x + 24 y - 1 = 0

x^{2} + 2 y^{2} = 1

What is 0.11x^2+0.25y^2=1 ?
The solution to 0.11x^2+0.25y^2=1 is Ellipse with (h,k)=(0,0),a=3.01511…,b=2