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

Popular >

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}

x^{2} + 6 x + 9 y^{2} - 36 y + 36 = 0

\frac{( x + 5 ) ^{2}}{25} + \frac{( y + 1 ) ^{2}}{36} = 1

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

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

\frac{x ^{2}}{5 ^{2}} + \frac{y ^{2}}{1 3 ^{2}} = 1

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