What is 25x^2+16y^2-100x-96y-156=0 ?

The solution to 25x^2+16y^2-100x-96y-156=0 is Ellipse with (h,k)=(2,3),a=4,b=5

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25x^2+16y^2-100x-96y-156=0

25 x^{2} + 16 y^{2} - 100 x - 96 y - 156 = 0

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

Solution steps

25 x^{2} + 16 y^{2} - 100 x - 96 y - 156 = 0

Rewrite

25 x^{2} + 16 y^{2} - 100 x - 96 y - 156 = 0

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

\frac{x ^{2}}{25} + \frac{( y - 3 ) ^{2}}{16} = 1

\frac{( x + 2 ) ^{2}}{25} + \frac{( y + 1 ) ^{2}}{4} = 1

16 - x^{2} - 4 y^{2} > 0

9 X^{2} + 4 Y^{2} - 24 Y = 0

9 x^{2} + 4 y^{2} - 54 x - 8 y - 59 = 0

What is 25x^2+16y^2-100x-96y-156=0 ?
The solution to 25x^2+16y^2-100x-96y-156=0 is Ellipse with (h,k)=(2,3),a=4,b=5