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

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

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

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

(h, k) = (1, - 3), a = 2, b = 4

Solution steps

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

Rewrite

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

in the form of the standard ellipse equation

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

Therefore ellipse properties are:

(h, k) = (1, - 3), a = 2, b = 4

b > a

therefore

b

is semi-major axis and

a

is semi-minor axis

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

(x + 4)^{2} + (\frac{y - 41}{2})^{2} = \frac{421}{4}

\frac{x ^{2}}{4900} + \frac{y ^{2}}{2500} = 1

x^{2} + y^{2} - \frac{21}{8} x + \frac{19}{4} - \frac{525}{8} = 0

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

25 x^{2} + 16 y^{2} + 200 x + 64 y + 64 = 0

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