What is 4x^2-8x+9y^2-72y+112=0 ?

The solution to 4x^2-8x+9y^2-72y+112=0 is Ellipse with (h,k)=(1,4),a=3,b=2

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4x^2-8x+9y^2-72y+112=0

4 x^{2} - 8 x + 9 y^{2} - 72 y + 112 = 0

(h, k) = (1, 4), a = 3, b = 2

Solution steps

4 x^{2} - 8 x + 9 y^{2} - 72 y + 112 = 0

Rewrite

4 x^{2} - 8 x + 9 y^{2} - 72 y + 112 = 0

in the form of the standard ellipse equation

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

Therefore ellipse properties are:

(h, k) = (1, 4), a = 3, b = 2

a > b

therefore

a

is semi-major axis and

b

is semi-minor axis

Ellipse with center (h, k) = (1, 4), a = 3, b = 2

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

4 x^{2} + 81 y^{2} = 324

3 x^{2} + y^{2} + 20 x + 32 = 0

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

x^{2} + 2 z^{2} + 6 x - 8 z + 1 = 0

What is 4x^2-8x+9y^2-72y+112=0 ?
The solution to 4x^2-8x+9y^2-72y+112=0 is Ellipse with (h,k)=(1,4),a=3,b=2