What is 3x^2+2y^2-16x+15=0 ?

The solution to 3x^2+2y^2-16x+15=0 is Ellipse with (h,k)=(8/3 ,0),a=(sqrt(19))/3 ,b=sqrt(19/6)

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3x^2+2y^2-16x+15=0

3 x^{2} + 2 y^{2} - 16 x + 15 = 0

(h, k) = (\frac{8}{3}, 0), a = \frac{19}{3}, b = \frac{19}{6}

Solution steps

3 x^{2} + 2 y^{2} - 16 x + 15 = 0

Rewrite

3 x^{2} + 2 y^{2} - 16 x + 15 = 0

in the form of the standard ellipse equation

\frac{( x - \frac{8}{3} ) ^{2}}{( \frac{19}{3} ) ^{2}} + \frac{( y - 0 ) ^{2}}{( \frac{19}{6} ) ^{2}} = 1

Therefore ellipse properties are:

(h, k) = (\frac{8}{3}, 0), a = \frac{19}{3}, b = \frac{19}{6}

b > a

therefore

b

is semi-major axis and

a

is semi-minor axis

Ellipse with center (h, k) = (\frac{8}{3}, 0), b = \frac{19}{6}, a = \frac{19}{3}

\frac{x ^{2}}{400} + \frac{y ^{2}}{100} = 1

\frac{( x + 2 ) ^{2}}{25} + (\frac{( y + 2 )}{9})^{2} = 1

\frac{( x - 3 ) ^{2}}{7} + \frac{y ^{2}}{15} = 1

x^{2} - 6 x + 4 y^{2} + 16 y + 21 = 0

\frac{( x + 3 ) ^{2}}{16} + \frac{( y - 1 ) ^{2}}{25} = 1

What is 3x^2+2y^2-16x+15=0 ?
The solution to 3x^2+2y^2-16x+15=0 is Ellipse with (h,k)=(8/3 ,0),a=(sqrt(19))/3 ,b=sqrt(19/6)