What is 5x^2+2y^2=45 ?

The solution to 5x^2+2y^2=45 is Ellipse with (h,k)=(0,0),a=3,b=(3sqrt(5))/(sqrt(2))

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5x^2+2y^2=45

5 x^{2} + 2 y^{2} = 45

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

Solution steps

5 x^{2} + 2 y^{2} = 45

Rewrite

5 x^{2} + 2 y^{2} = 45

in the form of the standard ellipse equation

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

Therefore ellipse properties are:

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

b > a

therefore

b

is semi-major axis and

a

is semi-minor axis

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

\frac{( x + 3 ) ^{2}}{12} + \frac{( y - 2 ) ^{2}}{16} = 1

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

\frac{x ^{2}}{81} + \frac{y ^{2}}{100} = 1

25 (x + 1)^{2} + 16 (y - 3)^{2} = 400

9 y^{2} + 90 y + 4 x^{2} - 16 x + 205 = 0

What is 5x^2+2y^2=45 ?
The solution to 5x^2+2y^2=45 is Ellipse with (h,k)=(0,0),a=3,b=(3sqrt(5))/(sqrt(2))