What is 3x^2+2y^2-17x=0 ?

The solution to 3x^2+2y^2-17x=0 is Ellipse with (h,k)=(17/6 ,0),a= 17/6 ,b=(17)/(2sqrt(6))

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3x^2+2y^2-17x=0

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

(h, k) = (\frac{17}{6}, 0), a = \frac{17}{6}, b = \frac{17}{2 6}

Solution steps

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

Rewrite

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

in the form of the standard ellipse equation

\frac{( x - \frac{17}{6} ) ^{2}}{( \frac{17}{6} ) ^{2}} + \frac{( y - 0 ) ^{2}}{( \frac{17}{2 6} ) ^{2}} = 1

Therefore ellipse properties are:

(h, k) = (\frac{17}{6}, 0), a = \frac{17}{6}, b = \frac{17}{2 6}

b > a

therefore

b

is semi-major axis and

a

is semi-minor axis

Ellipse with center (h, k) = (\frac{17}{6}, 0), b = \frac{17}{2 6}, a = \frac{17}{6}

x^{2} + 4 y^{2} + 10 x + 24 y + 25 = 0

(x - 3)^{2} + 4 (y + 1)^{2} = 1

\frac{x ^{2}}{8} + \frac{y ^{2}}{a} = 1

2 x^{2} + 4 y^{2} + 6 x - 8 y - 5 = 0

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

What is 3x^2+2y^2-17x=0 ?
The solution to 3x^2+2y^2-17x=0 is Ellipse with (h,k)=(17/6 ,0),a= 17/6 ,b=(17)/(2sqrt(6))