What is 16x^2+192x+576+25y^2=1600 ?

The solution to 16x^2+192x+576+25y^2=1600 is Ellipse with (h,k)=(-6,0),a=10,b=8

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16x^2+192x+576+25y^2=1600

16 x^{2} + 192 x + 576 + 25 y^{2} = 1600

(h, k) = (- 6, 0), a = 10, b = 8

Solution steps

16 x^{2} + 192 x + 576 + 25 y^{2} = 1600

Rewrite

16 x^{2} + 192 x + 576 + 25 y^{2} = 1600

in the form of the standard ellipse equation

\frac{( x - ( - 6 ) ) ^{2}}{1 0 ^{2}} + \frac{( y - 0 ) ^{2}}{8 ^{2}} = 1

Therefore ellipse properties are:

(h, k) = (- 6, 0), a = 10, b = 8

a > b

therefore

a

is semi-major axis and

b

is semi-minor axis

Ellipse with center (h, k) = (- 6, 0), a = 10, b = 8

x^{2} + y^{2} - 10 x - 10 y + 25 = 0

x^{2} - y^{2} = 1

x^{2} + y^{2} - 32 x - 60 y + 1122 = 0

x^{2}

\frac{x ^{2}}{36} + \frac{y ^{2}}{9} = 1

What is 16x^2+192x+576+25y^2=1600 ?
The solution to 16x^2+192x+576+25y^2=1600 is Ellipse with (h,k)=(-6,0),a=10,b=8