What is (4x^2-8x)+(9y^2-36y)=-4 ?

The solution to (4x^2-8x)+(9y^2-36y)=-4 is Ellipse with (h,k)=(1,2),a=3,b=2

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(4x^2-8x)+(9y^2-36y)=-4

(4 x^{2} - 8 x) + (9 y^{2} - 36 y) = - 4

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

Solution steps

4 x^{2} - 8 x + (9 y^{2} - 36 y) = - 4

Rewrite

4 x^{2} - 8 x + (9 y^{2} - 36 y) = - 4

in the form of the standard ellipse equation

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

Therefore ellipse properties are:

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

a > b

therefore

a

is semi-major axis and

b

is semi-minor axis

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

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

\frac{x ^{2}}{1 ^{2}} + \frac{y ^{2}}{0.4375 ^{2}} = 1

22 x^{2} + 66 y^{2} + 60 x + 4 y - 9 = 0

x^{2} + 2 y^{2} - 5 = 1

\frac{x ^{2}}{841} + \frac{y ^{2}}{484} = 1

What is (4x^2-8x)+(9y^2-36y)=-4 ?
The solution to (4x^2-8x)+(9y^2-36y)=-4 is Ellipse with (h,k)=(1,2),a=3,b=2