What is -1.14y^2=52.3+x^2 ?

The solution to -1.14y^2=52.3+x^2 is Ellipse with (h,k)=(0,0),a=7.23187…,b=6.77327…

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-1.14y^2=52.3+x^2

- 1.14 y^{2} = 52.3 + x^{2}

(h, k) = (0, 0), a = 7.23187 \dots, b = 6.77327 \dots

Solution steps

- 1.14 y^{2} = 52.3 + x^{2}

Rewrite

- 1.14 y^{2} = 52.3 + x^{2}

in the form of the standard ellipse equation

\frac{( x - 0 ) ^{2}}{7.23187 \dots ^{2}} + \frac{( y - 0 ) ^{2}}{6.77327 \dots ^{2}} = 1

Therefore ellipse properties are:

(h, k) = (0, 0), a = 7.23187 \dots, b = 6.77327 \dots

a > b

therefore

a

is semi-major axis and

b

is semi-minor axis

Ellipse with center (h, k) = (0, 0), a = 7.23187 \dots, b = 6.77327 \dots

\frac{( x - 3 ) ^{2}}{\frac{2}{9}} + \frac{( y - 5 ) ^{2}}{25} = 1

5 x^{2} - 70 x + 9 y^{2} + 90 y + 425 = 0

(\frac{y - 3}{64})^{2} + \frac{( x + 5 ) ^{2}}{81} = 1

4 x^{2} + 9 y^{2} + 8 x + 18 y - 23 = 0

4 x^{2} + 9 y^{2} - 48 x + 72 y - 144 = 0

What is -1.14y^2=52.3+x^2 ?
The solution to -1.14y^2=52.3+x^2 is Ellipse with (h,k)=(0,0),a=7.23187…,b=6.77327…