What is 25x^2+16y^2+100x-96y=156 ?

The solution to 25x^2+16y^2+100x-96y=156 is Ellipse with (h,k)=(-2,3),a=4,b=5

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25x^2+16y^2+100x-96y=156

25 x^{2} + 16 y^{2} + 100 x - 96 y = 156

(h, k) = (- 2, 3), a = 4, b = 5

Solution steps

25 x^{2} + 16 y^{2} + 100 x - 96 y = 156

Rewrite

25 x^{2} + 16 y^{2} + 100 x - 96 y = 156

in the form of the standard ellipse equation

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

Therefore ellipse properties are:

(h, k) = (- 2, 3), a = 4, b = 5

b > a

therefore

b

is semi-major axis and

a

is semi-minor axis

Ellipse with center (h, k) = (- 2, 3), b = 5, a = 4

x^{2} + 9 y^{2} - 8 x + 36 y + 4 = 0

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

9 x^{2} - 54 x + y^{2} - 2 y = - 81

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

3 x^{2} + y^{2} = 52

What is 25x^2+16y^2+100x-96y=156 ?
The solution to 25x^2+16y^2+100x-96y=156 is Ellipse with (h,k)=(-2,3),a=4,b=5