What is 25x^2+16y^2-200x-160y+400=0 ?

The solution to 25x^2+16y^2-200x-160y+400=0 is Ellipse with (h,k)=(4,5),a=4,b=5

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25x^2+16y^2-200x-160y+400=0

25 x^{2} + 16 y^{2} - 200 x - 160 y + 400 = 0

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

Solution steps

25 x^{2} + 16 y^{2} - 200 x - 160 y + 400 = 0

Rewrite

25 x^{2} + 16 y^{2} - 200 x - 160 y + 400 = 0

in the form of the standard ellipse equation

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

Therefore ellipse properties are:

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

b > a

therefore

b

is semi-major axis and

a

is semi-minor axis

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

\frac{x ^{2}}{64} + \frac{( y - 6 ) ^{2}}{121} = 1

4 x^{(2)} + y^{(2)} = 2 y

\frac{x ^{2}}{49} + \frac{y ^{2}}{40} = 1

3 = \frac{x ^{2}}{4} + \frac{y ^{2}}{9}

\frac{( x - 3 ) ^{2}}{49} + \frac{( y - 5 ) ^{2}}{16} = 1

What is 25x^2+16y^2-200x-160y+400=0 ?
The solution to 25x^2+16y^2-200x-160y+400=0 is Ellipse with (h,k)=(4,5),a=4,b=5