What is 4x^2-6x+y^2+2y=-1 ?

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

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4x^2-6x+y^2+2y=-1

4 x^{2} - 6 x + y^{2} + 2 y = - 1

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

Solution steps

4 x^{2} - 6 x + y^{2} + 2 y = - 1

Rewrite

4 x^{2} - 6 x + y^{2} + 2 y = - 1

in the form of the standard ellipse equation

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

Therefore ellipse properties are:

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

b > a

therefore

b

is semi-major axis and

a

is semi-minor axis

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

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