What is 4X^2+6Y^2-24X+2Y-12=0 ?

The solution to 4X^2+6Y^2-24X+2Y-12=0 is Ellipse with (h,k)=(3,-1/6),a=(17)/(2sqrt(6)),b= 17/6

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4X^2+6Y^2-24X+2Y-12=0

4 X^{2} + 6 Y^{2} - 24 X + 2 Y - 12 = 0

(h, k) = (3, - \frac{1}{6}), a = \frac{17}{2 6}, b = \frac{17}{6}

Solution steps

4 X^{2} + 6 Y^{2} - 24 X + 2 Y - 12 = 0

Rewrite

4 X^{2} + 6 Y^{2} - 24 X + 2 Y - 12 = 0

in the form of the standard ellipse equation

\frac{( X - 3 ) ^{2}}{( \frac{17}{2 6} ) ^{2}} + \frac{( Y - ( - \frac{1}{6} ) ) ^{2}}{( \frac{17}{6} ) ^{2}} = 1

Therefore ellipse properties are:

(h, k) = (3, - \frac{1}{6}), a = \frac{17}{2 6}, b = \frac{17}{6}

a > b

therefore

a

is semi-major axis and

b

is semi-minor axis

Ellipse with center (h, k) = (3, - \frac{1}{6}), a = \frac{17}{2 6}, b = \frac{17}{6}

25 y^{2} + 16 x^{2} + 50 y - 64 x - 311 = 0

25 x^{2} + 100 y^{2} = 400

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

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

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

What is 4X^2+6Y^2-24X+2Y-12=0 ?
The solution to 4X^2+6Y^2-24X+2Y-12=0 is Ellipse with (h,k)=(3,-1/6),a=(17)/(2sqrt(6)),b= 17/6