What is 16x^2+25y^2-224x-150y+1009=400 ?

The solution to 16x^2+25y^2-224x-150y+1009=400 is Ellipse with (h,k)=(7,3),a=5,b=4

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16x^2+25y^2-224x-150y+1009=400

16 x^{2} + 25 y^{2} - 224 x - 150 y + 1009 = 400

(h, k) = (7, 3), a = 5, b = 4

Solution steps

16 x^{2} + 25 y^{2} - 224 x - 150 y + 1009 = 400

Rewrite

16 x^{2} + 25 y^{2} - 224 x - 150 y + 1009 = 400

in the form of the standard ellipse equation

\frac{( x - 7 ) ^{2}}{5 ^{2}} + \frac{( y - 3 ) ^{2}}{4 ^{2}} = 1

Therefore ellipse properties are:

(h, k) = (7, 3), a = 5, b = 4

a > b

therefore

a

is semi-major axis and

b

is semi-minor axis

Ellipse with center (h, k) = (7, 3), a = 5, b = 4

\frac{( x - 2 ) ^{2}}{4} + \frac{( y + 2 ) ^{2}}{8} = 1

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

4 x^{2} + 25 y^{2} + 24 x + 250 y = - 561

x^{2} - 8 x + 16 y^{2} - 2 y + 4 = 625

9 x^{2} + 25 y^{2} - 36 x - 50 y - 164 = 0

What is 16x^2+25y^2-224x-150y+1009=400 ?
The solution to 16x^2+25y^2-224x-150y+1009=400 is Ellipse with (h,k)=(7,3),a=5,b=4