What is 4x^2+9y^2-8x+3y+4=0 ?

The solution to 4x^2+9y^2-8x+3y+4=0 is Ellipse with (h,k)=(1,-1/6),a= 1/4 ,b= 1/6

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4x^2+9y^2-8x+3y+4=0

4 x^{2} + 9 y^{2} - 8 x + 3 y + 4 = 0

(h, k) = (1, - \frac{1}{6}), a = \frac{1}{4}, b = \frac{1}{6}

Solution steps

4 x^{2} + 9 y^{2} - 8 x + 3 y + 4 = 0

Rewrite

4 x^{2} + 9 y^{2} - 8 x + 3 y + 4 = 0

in the form of the standard ellipse equation

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

Therefore ellipse properties are:

(h, k) = (1, - \frac{1}{6}), a = \frac{1}{4}, b = \frac{1}{6}

a > b

therefore

a

is semi-major axis and

b

is semi-minor axis

Ellipse with center (h, k) = (1, - \frac{1}{6}), a = \frac{1}{4}, b = \frac{1}{6}

\frac{( x - 2 ) ^{2}}{4} + \frac{( y + 1 ) ^{2}}{9} = 1

x^{2} + 4 y^{2} + 4 x - 12 = 0

12 x^{2} + 5 y^{2} - 60 = 0

9 x^{2} + 16 y^{2} + 96 y - 36 x + 36 = 0

4 x^{2} + 8 x + 3 y^{2} + 6 y - 17 = 0

What is 4x^2+9y^2-8x+3y+4=0 ?
The solution to 4x^2+9y^2-8x+3y+4=0 is Ellipse with (h,k)=(1,-1/6),a= 1/4 ,b= 1/6