What is 3x^2+5y+5y^2=5 ?

The solution to 3x^2+5y+5y^2=5 is Ellipse with (h,k)=(0,-1/2),a= 5/(2sqrt(3)),b=(sqrt(5))/2

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3x^2+5y+5y^2=5

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

(h, k) = (0, - \frac{1}{2}), a = \frac{5}{2 3}, b = \frac{5}{2}

Solution steps

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

Rewrite

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

in the form of the standard ellipse equation

\frac{( x - 0 ) ^{2}}{( \frac{5}{2 3} ) ^{2}} + \frac{( y - ( - \frac{1}{2} ) ) ^{2}}{( \frac{5}{2} ) ^{2}} = 1

Therefore ellipse properties are:

(h, k) = (0, - \frac{1}{2}), a = \frac{5}{2 3}, b = \frac{5}{2}

a > b

therefore

a

is semi-major axis and

b

is semi-minor axis

Ellipse with center (h, k) = (0, - \frac{1}{2}), a = \frac{5}{2 3}, b = \frac{5}{2}

\frac{( x - 6 ) ^{2}}{36} + \frac{( y + 4 ) ^{2}}{16} = 1

49 x^{2} + 9 y^{2} = 16

\frac{( x - 3 ) ^{2}}{36} + \frac{( y - 3 ) ^{2}}{32} = 1

x^{2} + 4 y^{2} - 20 x + 84 = 0

(x^{2} + y^{2} - 16 x + 8 y + 80) = 4 (x^{2} + y^{2} - 4 x - 8 y + 20)

What is 3x^2+5y+5y^2=5 ?
The solution to 3x^2+5y+5y^2=5 is Ellipse with (h,k)=(0,-1/2),a= 5/(2sqrt(3)),b=(sqrt(5))/2