What is 9x^2+25y^2-144x+200y+751=0 ?

The solution to 9x^2+25y^2-144x+200y+751=0 is Ellipse with (h,k)=(8,-4),a=5,b=3

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9x^2+25y^2-144x+200y+751=0

9 x^{2} + 25 y^{2} - 144 x + 200 y + 751 = 0

(h, k) = (8, - 4), a = 5, b = 3

Solution steps

9 x^{2} + 25 y^{2} - 144 x + 200 y + 751 = 0

Rewrite

9 x^{2} + 25 y^{2} - 144 x + 200 y + 751 = 0

in the form of the standard ellipse equation

\frac{( x - 8 ) ^{2}}{5 ^{2}} + \frac{( y - ( - 4 ) ) ^{2}}{3 ^{2}} = 1

Therefore ellipse properties are:

(h, k) = (8, - 4), a = 5, b = 3

a > b

therefore

a

is semi-major axis and

b

is semi-minor axis

Ellipse with center (h, k) = (8, - 4), a = 5, b = 3

\frac{4 x ^{2}}{19} + \frac{2 y ^{2}}{19} = 1

2 x - x^{2} - 4 y^{2} - 16 y - 1 = 0

\frac{( x - 4 ) ^{2}}{16} + \frac{y ^{2}}{40.96} = 1

2 x^{2} + 2 y^{2} - 28 y = 0

(x + 2)^{2} 16 + \frac{( y + 2 ) ^{2}}{25} = 1

What is 9x^2+25y^2-144x+200y+751=0 ?
The solution to 9x^2+25y^2-144x+200y+751=0 is Ellipse with (h,k)=(8,-4),a=5,b=3