What is 9x^2+5y^2-18x-20y-151=0 ?

The solution to 9x^2+5y^2-18x-20y-151=0 is Ellipse with (h,k)=(1,2),a=2sqrt(5),b=6

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9x^2+5y^2-18x-20y-151=0

9 x^{2} + 5 y^{2} - 18 x - 20 y - 151 = 0

(h, k) = (1, 2), a = 25, b = 6

Solution steps

9 x^{2} + 5 y^{2} - 18 x - 20 y - 151 = 0

Rewrite

9 x^{2} + 5 y^{2} - 18 x - 20 y - 151 = 0

in the form of the standard ellipse equation

\frac{( x - 1 ) ^{2}}{( 2 5 ) ^{2}} + \frac{( y - 2 ) ^{2}}{6 ^{2}} = 1

Therefore ellipse properties are:

(h, k) = (1, 2), a = 25, b = 6

b > a

therefore

b

is semi-major axis and

a

is semi-minor axis

Ellipse with center (h, k) = (1, 2), b = 6, a = 25

\frac{x ^{2}}{4} + \frac{( y - 5 ) ^{2}}{5} = 1

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

5 x^{2} + 3 y^{2} - 12 = 0

4 x^{2} + y^{2} + 8 x = 0

28 x^{2} + 64 y^{2} - 28 x + 128 y - 377 = 0

What is 9x^2+5y^2-18x-20y-151=0 ?
The solution to 9x^2+5y^2-18x-20y-151=0 is Ellipse with (h,k)=(1,2),a=2sqrt(5),b=6