What is 3x^2+4y^2+6x-8y-5=0 ?

The solution to 3x^2+4y^2+6x-8y-5=0 is Ellipse with (h,k)=(-1,1),a=2,b=sqrt(3)

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3x^2+4y^2+6x-8y-5=0

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

(h, k) = (- 1, 1), a = 2, b = 3

Solution steps

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

Rewrite

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

in the form of the standard ellipse equation

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

Therefore ellipse properties are:

(h, k) = (- 1, 1), a = 2, b = 3

a > b

therefore

a

is semi-major axis and

b

is semi-minor axis

Ellipse with center (h, k) = (- 1, 1), a = 2, b = 3

27 x^{2} + 36 y^{2} + 108 x - 144 y - 720 = 0

\frac{x ^{2}}{2 ^{2}} + \frac{y ^{2}}{2 - 16} = 1

6 = 8 x^{2} + y^{2}

4 x^{2} + 7 y^{2} < 28

x^{2} + 9 y^{2} - 8 x + 36 y - 2 = 0

What is 3x^2+4y^2+6x-8y-5=0 ?
The solution to 3x^2+4y^2+6x-8y-5=0 is Ellipse with (h,k)=(-1,1),a=2,b=sqrt(3)