What is 112x^2+144y^2-896x+864y=-2080 ?

The solution to 112x^2+144y^2-896x+864y=-2080 is Ellipse with (h,k)=(4,-3),a=3,b=sqrt(7)

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112x^2+144y^2-896x+864y=-2080

112 x^{2} + 144 y^{2} - 896 x + 864 y = - 2080

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

Solution steps

112 x^{2} + 144 y^{2} - 896 x + 864 y = - 2080

Rewrite

112 x^{2} + 144 y^{2} - 896 x + 864 y = - 2080

in the form of the standard ellipse equation

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

Therefore ellipse properties are:

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

a > b

therefore

a

is semi-major axis and

b

is semi-minor axis

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

8 x^{2} + y^{2} = 1

9 = 4 x^{2} + z^{2}

\frac{x ^{2}}{4} + \frac{y ^{2}}{6} = 1

9 x^{2} + 16 y^{2} - 54 x - 64 y + 1 = 0

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

What is 112x^2+144y^2-896x+864y=-2080 ?
The solution to 112x^2+144y^2-896x+864y=-2080 is Ellipse with (h,k)=(4,-3),a=3,b=sqrt(7)