What is 4x^2+6y^2-8x+4y-6=0 ?

The solution to 4x^2+6y^2-8x+4y-6=0 is Ellipse with (h,k)=(1,-1/3),a=(2sqrt(2))/(sqrt(3)),b= 4/3

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4x^2+6y^2-8x+4y-6=0

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

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

Solution steps

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

Rewrite

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

in the form of the standard ellipse equation

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

Therefore ellipse properties are:

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

a > b

therefore

a

is semi-major axis and

b

is semi-minor axis

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

y^{2} = x (4 - x) 2

25 x^{2} + 16 y^{2} + 50 x - 96 y - 231 = 0

4 x^{2} + y^{2} - 24 x + 4 y + 24 = 0

\frac{x - 3 y}{x ^{2} + y ^{2}} + 1 = 0

a^{2} + \frac{a ^{2}}{2} + \frac{b ^{2}}{2} = 26

What is 4x^2+6y^2-8x+4y-6=0 ?
The solution to 4x^2+6y^2-8x+4y-6=0 is Ellipse with (h,k)=(1,-1/3),a=(2sqrt(2))/(sqrt(3)),b= 4/3