What is 25x^2+y^2-100x+8y+91=0 ?

The solution to 25x^2+y^2-100x+8y+91=0 is Ellipse with (h,k)=(2,-4),a=1,b=5

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25x^2+y^2-100x+8y+91=0

25 x^{2} + y^{2} - 100 x + 8 y + 91 = 0

(h, k) = (2, - 4), a = 1, b = 5

Solution steps

25 x^{2} + y^{2} - 100 x + 8 y + 91 = 0

Rewrite

25 x^{2} + y^{2} - 100 x + 8 y + 91 = 0

in the form of the standard ellipse equation

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

Therefore ellipse properties are:

(h, k) = (2, - 4), a = 1, b = 5

b > a

therefore

b

is semi-major axis and

a

is semi-minor axis

Ellipse with center (h, k) = (2, - 4), b = 5, a = 1

\frac{9 x ^{2}}{25} + \frac{16 y ^{2}}{25} < 1

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

49 x^{2} + 16 y^{2} = 784

\frac{( x - 6 ) ^{2}}{36} + \frac{( y + 1 ) ^{2}}{25} = 1

x^{2} + 4 y^{2} - 2 x - 16 y + 13 = 0

What is 25x^2+y^2-100x+8y+91=0 ?
The solution to 25x^2+y^2-100x+8y+91=0 is Ellipse with (h,k)=(2,-4),a=1,b=5