What is x^2+5y^2-30y+25=0 ?

The solution to x^2+5y^2-30y+25=0 is Ellipse with (h,k)=(0,3),a=2sqrt(5),b=2

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x^2+5y^2-30y+25=0

x^{2} + 5 y^{2} - 30 y + 25 = 0

(h, k) = (0, 3), a = 25, b = 2

Solution steps

x^{2} + 5 y^{2} - 30 y + 25 = 0

Rewrite

x^{2} + 5 y^{2} - 30 y + 25 = 0

in the form of the standard ellipse equation

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

Therefore ellipse properties are:

(h, k) = (0, 3), a = 25, b = 2

a > b

therefore

a

is semi-major axis and

b

is semi-minor axis

Ellipse with center (h, k) = (0, 3), a = 25, b = 2

3 x^{2} + 9 y^{2} - 6 x - 7 y - 8 = 0

\frac{x ^{2}}{25} + \frac{y ^{2}}{39} = 1

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

\frac{( x - 81 ) ^{2}}{6 4 ^{2}} + \frac{( y - 64 ) ^{2}}{8 1 ^{2}} = 1

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

What is x^2+5y^2-30y+25=0 ?
The solution to x^2+5y^2-30y+25=0 is Ellipse with (h,k)=(0,3),a=2sqrt(5),b=2