What is 25x^2+4y^2-50x+40y=-25 ?

The solution to 25x^2+4y^2-50x+40y=-25 is Ellipse with (h,k)=(1,-5),a=2,b=5

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25x^2+4y^2-50x+40y=-25

25 x^{2} + 4 y^{2} - 50 x + 40 y = - 25

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

Solution steps

25 x^{2} + 4 y^{2} - 50 x + 40 y = - 25

Rewrite

25 x^{2} + 4 y^{2} - 50 x + 40 y = - 25

in the form of the standard ellipse equation

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

Therefore ellipse properties are:

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

b > a

therefore

b

is semi-major axis and

a

is semi-minor axis

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

What is 25x^2+4y^2-50x+40y=-25 ?
The solution to 25x^2+4y^2-50x+40y=-25 is Ellipse with (h,k)=(1,-5),a=2,b=5