What is 25x^2+16y^2-250x-32y+241=0 ?

The solution to 25x^2+16y^2-250x-32y+241=0 is Ellipse with (h,k)=(5,1),a=4,b=5

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25x^2+16y^2-250x-32y+241=0

25 x^{2} + 16 y^{2} - 250 x - 32 y + 241 = 0

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

Solution steps

25 x^{2} + 16 y^{2} - 250 x - 32 y + 241 = 0

Rewrite

25 x^{2} + 16 y^{2} - 250 x - 32 y + 241 = 0

in the form of the standard ellipse equation

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

Therefore ellipse properties are:

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

b > a

therefore

b

is semi-major axis and

a

is semi-minor axis

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

9 x^{2} + 5 y^{2} = 45

\frac{( x - 1 ) ^{2}}{9} + \frac{( y - 2 ) ^{2}}{4} = 1

25 x^{2} + 12 y^{2} + 20 x - 12 y = 4

9 x^{2} + 4 y^{2} - 18 x + 24 y + 9 = 0

(\frac{( x + 3 )}{16})^{2} + \frac{( y - 5 ) ^{2}}{25} = 1

What is 25x^2+16y^2-250x-32y+241=0 ?
The solution to 25x^2+16y^2-250x-32y+241=0 is Ellipse with (h,k)=(5,1),a=4,b=5