What is 25x^{(2)}+4y^{(2)}=99 ?

The solution to 25x^{(2)}+4y^{(2)}=99 is Ellipse with (h,k)=(0,0),a=(3sqrt(11))/5 ,b=(3sqrt(11))/2

Popular >

25x^{(2)}+4y^{(2)}=99

25 x^{(2)} + 4 y^{(2)} = 99

(h, k) = (0, 0), a = \frac{3 11}{5}, b = \frac{3 11}{2}

Solution steps

25 x^{2} + 4 y^{2} = 99

Rewrite

25 x^{2} + 4 y^{2} = 99

in the form of the standard ellipse equation

\frac{( x - 0 ) ^{2}}{( \frac{3 11}{5} ) ^{2}} + \frac{( y - 0 ) ^{2}}{( \frac{3 11}{2} ) ^{2}} = 1

Therefore ellipse properties are:

(h, k) = (0, 0), a = \frac{3 11}{5}, b = \frac{3 11}{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 11}{2}, a = \frac{3 11}{5}

3 x^{2} - 9 x + 2 y^{2} + 10 y - 6 = 0

x^{2} + y^{2} = 10 - x^{2} - 2 y^{2}

- \frac{x ^{2}}{9} - y^{2} = 1

5 x^{2} + 72 y^{2} - 2 > 0

128 + 16 y - x^{2} - 4 y^{2} \geq 0

What is 25x^{(2)}+4y^{(2)}=99 ?
The solution to 25x^{(2)}+4y^{(2)}=99 is Ellipse with (h,k)=(0,0),a=(3sqrt(11))/5 ,b=(3sqrt(11))/2