What is 3x^2+4y^2-5x+2y+1=0 ?

The solution to 3x^2+4y^2-5x+2y+1=0 is Ellipse with (h,k)=(5/6 ,-1/4),a= 2/3 ,b=sqrt(1/3)

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3x^2+4y^2-5x+2y+1=0

3 x^{2} + 4 y^{2} - 5 x + 2 y + 1 = 0

(h, k) = (\frac{5}{6}, - \frac{1}{4}), a = \frac{2}{3}, b = \frac{1}{3}

Solution steps

3 x^{2} + 4 y^{2} - 5 x + 2 y + 1 = 0

Rewrite

3 x^{2} + 4 y^{2} - 5 x + 2 y + 1 = 0

in the form of the standard ellipse equation

\frac{( x - \frac{5}{6} ) ^{2}}{( \frac{2}{3} ) ^{2}} + \frac{( y - ( - \frac{1}{4} ) ) ^{2}}{( \frac{1}{3} ) ^{2}} = 1

Therefore ellipse properties are:

(h, k) = (\frac{5}{6}, - \frac{1}{4}), a = \frac{2}{3}, b = \frac{1}{3}

a > b

therefore

a

is semi-major axis and

b

is semi-minor axis

Ellipse with center (h, k) = (\frac{5}{6}, - \frac{1}{4}), a = \frac{2}{3}, b = \frac{1}{3}

\frac{x ^{2}}{36} + \frac{y ^{2}}{121} = 1

(x + 8)^{2} + (\frac{y + 1}{2})^{2} = 3

4 x^{2} + y^{2} - 8 x + 6 y + 9 = 0

\frac{( x + 3 ) ^{2}}{24} + \frac{( y - 5 ) ^{2}}{49} = 1

\frac{( x + 3 ) ^{2}}{64} + \frac{( y - 6 ) ^{2}}{100} = 1

What is 3x^2+4y^2-5x+2y+1=0 ?
The solution to 3x^2+4y^2-5x+2y+1=0 is Ellipse with (h,k)=(5/6 ,-1/4),a= 2/3 ,b=sqrt(1/3)