What is 25x^2+4y^2-100x+8y+91=0 ?

The solution to 25x^2+4y^2-100x+8y+91=0 is Ellipse with (h,k)=(2,-1),a=(sqrt(13))/5 ,b=(sqrt(13))/2

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25x^2+4y^2-100x+8y+91=0

25 x^{2} + 4 y^{2} - 100 x + 8 y + 91 = 0

(h, k) = (2, - 1), a = \frac{13}{5}, b = \frac{13}{2}

Solution steps

25 x^{2} + 4 y^{2} - 100 x + 8 y + 91 = 0

Rewrite

25 x^{2} + 4 y^{2} - 100 x + 8 y + 91 = 0

in the form of the standard ellipse equation

\frac{( x - 2 ) ^{2}}{( \frac{13}{5} ) ^{2}} + \frac{( y - ( - 1 ) ) ^{2}}{( \frac{13}{2} ) ^{2}} = 1

Therefore ellipse properties are:

(h, k) = (2, - 1), a = \frac{13}{5}, b = \frac{13}{2}

b > a

therefore

b

is semi-major axis and

a

is semi-minor axis

Ellipse with center (h, k) = (2, - 1), b = \frac{13}{2}, a = \frac{13}{5}

What is 25x^2+4y^2-100x+8y+91=0 ?
The solution to 25x^2+4y^2-100x+8y+91=0 is Ellipse with (h,k)=(2,-1),a=(sqrt(13))/5 ,b=(sqrt(13))/2