What is 25x^2+16y^2+100x-32y-284=0 ?

The solution to 25x^2+16y^2+100x-32y-284=0 is Ellipse with (h,k)=(-2,1),a=4,b=5

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25x^2+16y^2+100x-32y-284=0

25 x^{2} + 16 y^{2} + 100 x - 32 y - 284 = 0

(h, k) = (- 2, 1), a = 4, b = 5

Solution steps

25 x^{2} + 16 y^{2} + 100 x - 32 y - 284 = 0

Rewrite

25 x^{2} + 16 y^{2} + 100 x - 32 y - 284 = 0

in the form of the standard ellipse equation

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

Therefore ellipse properties are:

(h, k) = (- 2, 1), a = 4, b = 5

b > a

therefore

b

is semi-major axis and

a

is semi-minor axis

Ellipse with center (h, k) = (- 2, 1), b = 5, a = 4

x^{2} + 3 y^{2} - 3 x - 5 y = 0

x^{2} - 2 x + 4 y^{2} - 24 y + 33 = 0

\frac{x ^{2}}{1} + \frac{y ^{2}}{5} = 1

4 x^{2} + y^{2} + 56 = 4 y - 56 x

\frac{( x - 3 ) ^{2}}{49} + \frac{( y + 6 ) ^{2}}{100} = 1

What is 25x^2+16y^2+100x-32y-284=0 ?
The solution to 25x^2+16y^2+100x-32y-284=0 is Ellipse with (h,k)=(-2,1),a=4,b=5