What is 49x^2+16y^2+196x-96y=444 ?

The solution to 49x^2+16y^2+196x-96y=444 is Ellipse with (h,k)=(-2,3),a=4,b=7

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49x^2+16y^2+196x-96y=444

49 x^{2} + 16 y^{2} + 196 x - 96 y = 444

(h, k) = (- 2, 3), a = 4, b = 7

Solution steps

49 x^{2} + 16 y^{2} + 196 x - 96 y = 444

Rewrite

49 x^{2} + 16 y^{2} + 196 x - 96 y = 444

in the form of the standard ellipse equation

\frac{( x - ( - 2 ) ) ^{2}}{4 ^{2}} + \frac{( y - 3 ) ^{2}}{7 ^{2}} = 1

Therefore ellipse properties are:

(h, k) = (- 2, 3), a = 4, b = 7

b > a

therefore

b

is semi-major axis and

a

is semi-minor axis

Ellipse with center (h, k) = (- 2, 3), b = 7, a = 4

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

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

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

\frac{x ^{2}}{49} + \frac{y ^{2}}{81} = 1

3 x^{2} + 5 y^{2} - 6 x + 2 y - 9 = 0

What is 49x^2+16y^2+196x-96y=444 ?
The solution to 49x^2+16y^2+196x-96y=444 is Ellipse with (h,k)=(-2,3),a=4,b=7