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

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

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

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

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

Solution steps

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

Rewrite

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

in the form of the standard ellipse equation

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

Therefore ellipse properties are:

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

b > a

therefore

b

is semi-major axis and

a

is semi-minor axis

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

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

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

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