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

9 x^{2} + 4 y^{2} - 18 x - 24 y + 9 = 0

3 y^{2} = - x^{2} - 4 x + 8

3 x^{2} + 4 y^{2} + 18 x - 16 y + 31 = 0

\frac{x ^{2}}{8} + \frac{y ^{2}}{2} = 1

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