What is 4x^2-2x+9y^2+6y=41 ?

The solution to 4x^2-2x+9y^2+6y=41 is Ellipse with (h,k)=(1/4 ,-1/3),a= 13/4 ,b= 13/6

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4x^2-2x+9y^2+6y=41

4 x^{2} - 2 x + 9 y^{2} + 6 y = 41

(h, k) = (\frac{1}{4}, - \frac{1}{3}), a = \frac{13}{4}, b = \frac{13}{6}

Solution steps

4 x^{2} - 2 x + 9 y^{2} + 6 y = 41

Rewrite

4 x^{2} - 2 x + 9 y^{2} + 6 y = 41

in the form of the standard ellipse equation

\frac{( x - \frac{1}{4} ) ^{2}}{( \frac{13}{4} ) ^{2}} + \frac{( y - ( - \frac{1}{3} ) ) ^{2}}{( \frac{13}{6} ) ^{2}} = 1

Therefore ellipse properties are:

(h, k) = (\frac{1}{4}, - \frac{1}{3}), a = \frac{13}{4}, b = \frac{13}{6}

a > b

therefore

a

is semi-major axis and

b

is semi-minor axis

Ellipse with center (h, k) = (\frac{1}{4}, - \frac{1}{3}), a = \frac{13}{4}, b = \frac{13}{6}

25 \cdot x^{2} + 9 \cdot y^{2} = 225

2 x^{2} + 5 y^{2} + 3 x + 5 y - 6 = 0

\frac{( x - 3 ) ^{2}}{16} + (\frac{y + 2}{9})^{2} = 1

\frac{( x + 4 ) ^{2}}{25} + \frac{( y + 1 ) ^{2}}{16} = 1

9 x^{2} + 16 y^{2} + 18 x - 64 y - 71 = 0

What is 4x^2-2x+9y^2+6y=41 ?
The solution to 4x^2-2x+9y^2+6y=41 is Ellipse with (h,k)=(1/4 ,-1/3),a= 13/4 ,b= 13/6