What is 5x^2+9y^2=100 ?

The solution to 5x^2+9y^2=100 is Ellipse with (h,k)=(0,0),a=2sqrt(5),b= 10/3

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5x^2+9y^2=100

5 x^{2} + 9 y^{2} = 100

(h, k) = (0, 0), a = 25, b = \frac{10}{3}

Solution steps

5 x^{2} + 9 y^{2} = 100

Rewrite

5 x^{2} + 9 y^{2} = 100

in the form of the standard ellipse equation

\frac{( x - 0 ) ^{2}}{( 2 5 ) ^{2}} + \frac{( y - 0 ) ^{2}}{( \frac{10}{3} ) ^{2}} = 1

Therefore ellipse properties are:

(h, k) = (0, 0), a = 25, b = \frac{10}{3}

a > b

therefore

a

is semi-major axis and

b

is semi-minor axis

Ellipse with center (h, k) = (0, 0), a = 25, b = \frac{10}{3}

\frac{( x ^{2} )}{( 4 )} + \frac{( ( y - 1 ) ^{2} )}{( 9 )} < 1

\frac{( x + 6 ) ^{2}}{7} + \frac{( y - 3 ) ^{2}}{16} = 1

4 x^{2} + y^{2} + 64 x - y + 201 = 0

5 x^{2} + 25 y^{2} - 125 = 0

- 6 y = x^{2} + y^{2}

What is 5x^2+9y^2=100 ?
The solution to 5x^2+9y^2=100 is Ellipse with (h,k)=(0,0),a=2sqrt(5),b= 10/3