x^2+9y^2=5

Solution

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

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

Solution steps

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

Rewrite

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

in the form of the standard ellipse equation

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

Therefore ellipse properties are:

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

a > b

therefore

a

is semi-major axis and

b

is semi-minor axis

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

9 x^{2} + 16 y^{2} + 18 x - 135 = 0

16 x^{2} + 4 y^{2} = 25

x^{2} + 9 y^{2} < 9

x^{2} + 4 y^{2} + 3 x + 2 y - 56 = 0

3 X^{2} + 4 Y^{2} + 12 X - 8 Y + 9 = 0

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