What is 25x^2+16y^2-100x-64y-236=0 ?

The solution to 25x^2+16y^2-100x-64y-236=0 is Ellipse with (h,k)=(2,2),a=4,b=5

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25x^2+16y^2-100x-64y-236=0

25 x^{2} + 16 y^{2} - 100 x - 64 y - 236 = 0

(h, k) = (2, 2), a = 4, b = 5

Solution steps

25 x^{2} + 16 y^{2} - 100 x - 64 y - 236 = 0

Rewrite

25 x^{2} + 16 y^{2} - 100 x - 64 y - 236 = 0

in the form of the standard ellipse equation

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

Therefore ellipse properties are:

(h, k) = (2, 2), a = 4, b = 5

b > a

therefore

b

is semi-major axis and

a

is semi-minor axis

Ellipse with center (h, k) = (2, 2), b = 5, a = 4

12 x - 5 y + 10 x^{2} + 25 = \frac{- ( 100 y ^{2} )}{10 + 3}

\frac{( x - 2 ) ^{2}}{9} + \frac{( y + 5 ) ^{2}}{36} = 1

2 y^{2} = - x^{2} + 4

16 x^{2} - 64 x + 9 y^{2} + 9 y + 1 = 0

\frac{( x + 5 ) ^{2}}{81} + \frac{( y - 1 ) ^{2}}{144} = 1

What is 25x^2+16y^2-100x-64y-236=0 ?
The solution to 25x^2+16y^2-100x-64y-236=0 is Ellipse with (h,k)=(2,2),a=4,b=5