What is 25x^2+4y^2-8y-50x=71 ?

The solution to 25x^2+4y^2-8y-50x=71 is Ellipse with (h,k)=(1,1),a=2,b=5

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25x^2+4y^2-8y-50x=71

25 x^{2} + 4 y^{2} - 8 y - 50 x = 71

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

Solution steps

25 x^{2} + 4 y^{2} - 8 y - 50 x = 71

Rewrite

25 x^{2} + 4 y^{2} - 8 y - 50 x = 71

in the form of the standard ellipse equation

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

Therefore ellipse properties are:

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

b > a

therefore

b

is semi-major axis and

a

is semi-minor axis

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

3 y^{2} = - 2 x^{2} + 1

12 x^{2} + 16 y^{2} = 192

\frac{x ^{2}}{c _{1}^{2}} = 1 - \frac{y ^{2}}{c _{2}^{2}}

16 x^{2} + 4 y^{2} - 32 x + 24 y - 12 = 0

x^{2} - 2 x + \frac{y ^{2}}{4} - y \leq 14

What is 25x^2+4y^2-8y-50x=71 ?
The solution to 25x^2+4y^2-8y-50x=71 is Ellipse with (h,k)=(1,1),a=2,b=5