What is 25x^2+y^2-100x-2y+76=0 ?

The solution to 25x^2+y^2-100x-2y+76=0 is Ellipse with (h,k)=(2,1),a=1,b=5

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25x^2+y^2-100x-2y+76=0

25 x^{2} + y^{2} - 100 x - 2 y + 76 = 0

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

Solution steps

25 x^{2} + y^{2} - 100 x - 2 y + 76 = 0

Rewrite

25 x^{2} + y^{2} - 100 x - 2 y + 76 = 0

in the form of the standard ellipse equation

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

Therefore ellipse properties are:

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

4 x^{2} + 3 y^{2} = 120

5 x^{2} + 9 y^{2} - 20 x + 54 y + 56 = 0

x^{2} + 4 y^{2} = 8

x^{2} + 9 y^{2} - 9 = 0

4 x^{2} + 9 y^{2} - 225 = 0

What is 25x^2+y^2-100x-2y+76=0 ?
The solution to 25x^2+y^2-100x-2y+76=0 is Ellipse with (h,k)=(2,1),a=1,b=5