What is 30x^2+9y^2=225 ?

The solution to 30x^2+9y^2=225 is Ellipse with (h,k)=(0,0),a=sqrt(15/2),b=5

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30x^2+9y^2=225

30 x^{2} + 9 y^{2} = 225

(h, k) = (0, 0), a = \frac{15}{2}, b = 5

Solution steps

30 x^{2} + 9 y^{2} = 225

Rewrite

30 x^{2} + 9 y^{2} = 225

in the form of the standard ellipse equation

\frac{( x - 0 ) ^{2}}{( \frac{15}{2} ) ^{2}} + \frac{( y - 0 ) ^{2}}{5 ^{2}} = 1

Therefore ellipse properties are:

(h, k) = (0, 0), a = \frac{15}{2}, b = 5

b > a

therefore

b

is semi-major axis and

a

is semi-minor axis

Ellipse with center (h, k) = (0, 0), b = 5, a = \frac{15}{2}

3 x^{2} + 8 y^{2} = 1

\frac{( x - 2.63 ) ^{2}}{1.34} + \frac{y ^{2}}{3.22} - 1 = 1

4 x^{2} + y^{2} - 32 x - 80 = 0

(x - \frac{2}{3})^{2} + 4 (y - 1)^{2} = 4

2 x^{2} + x + y^{2} - 6 = 0

What is 30x^2+9y^2=225 ?
The solution to 30x^2+9y^2=225 is Ellipse with (h,k)=(0,0),a=sqrt(15/2),b=5