What is 25x^2+49y^2+100x-392y-341=0 ?

The solution to 25x^2+49y^2+100x-392y-341=0 is Ellipse with (h,k)=(-2,4),a=7,b=5

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25x^2+49y^2+100x-392y-341=0

25 x^{2} + 49 y^{2} + 100 x - 392 y - 341 = 0

(h, k) = (- 2, 4), a = 7, b = 5

Solution steps

25 x^{2} + 49 y^{2} + 100 x - 392 y - 341 = 0

Rewrite

25 x^{2} + 49 y^{2} + 100 x - 392 y - 341 = 0

in the form of the standard ellipse equation

\frac{( x - ( - 2 ) ) ^{2}}{7 ^{2}} + \frac{( y - 4 ) ^{2}}{5 ^{2}} = 1

Therefore ellipse properties are:

(h, k) = (- 2, 4), a = 7, b = 5

a > b

therefore

a

is semi-major axis and

b

is semi-minor axis

Ellipse with center (h, k) = (- 2, 4), a = 7, b = 5

9 x^{2} + 25 y^{2} - 6 x - 25 y - 19 = 0

\frac{x ^{2}}{15} + \frac{y ^{2}}{16} = 1

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

64 x^{2} + 49 y^{2} = 3136

\frac{x ^{2}}{49} + \frac{y ^{2}}{64} = 1

What is 25x^2+49y^2+100x-392y-341=0 ?
The solution to 25x^2+49y^2+100x-392y-341=0 is Ellipse with (h,k)=(-2,4),a=7,b=5