What is x^2+4y^2-2.71=0 ?

The solution to x^2+4y^2-2.71=0 is Ellipse with (h,k)=(0,0),a=1.64620…,b=0.82310…

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x^2+4y^2-2.71=0

x^{2} + 4 y^{2} - 2.71 = 0

(h, k) = (0, 0), a = 1.64620 \dots, b = 0.82310 \dots

Solution steps

x^{2} + 4 y^{2} - 2.71 = 0

Rewrite

x^{2} + 4 y^{2} - 2.71 = 0

in the form of the standard ellipse equation

\frac{( x - 0 ) ^{2}}{1.64620 \dots ^{2}} + \frac{( y - 0 ) ^{2}}{0.82310 \dots ^{2}} = 1

Therefore ellipse properties are:

(h, k) = (0, 0), a = 1.64620 \dots, b = 0.82310 \dots

a > b

therefore

a

is semi-major axis and

b

is semi-minor axis

Ellipse with center (h, k) = (0, 0), a = 1.64620 \dots, b = 0.82310 \dots

\frac{( x - 5 ) ^{2}}{144} + \frac{( y + 2 ) ^{2}}{169} = 1

4 y^{(2)} + 2 x^{(2)} - 4 y - 8 x - 15 = 0

4 x^{2} + y^{2} + 8 x + 4 y - 4 = 0

\frac{x ^{2}}{1} + \frac{y ^{2}}{a - 16} = 1

9 x^{2} + 5 y^{2} - 18 x - 40 y + 44 = 0

What is x^2+4y^2-2.71=0 ?
The solution to x^2+4y^2-2.71=0 is Ellipse with (h,k)=(0,0),a=1.64620…,b=0.82310…