What is 4x^2+2x+y^2-10y=6 ?

The solution to 4x^2+2x+y^2-10y=6 is Ellipse with (h,k)=(-1/4 ,5),a=(5sqrt(5))/4 ,b=(5sqrt(5))/2

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4x^2+2x+y^2-10y=6

4 x^{2} + 2 x + y^{2} - 10 y = 6

(h, k) = (- \frac{1}{4}, 5), a = \frac{5 5}{4}, b = \frac{5 5}{2}

Solution steps

4 x^{2} + 2 x + y^{2} - 10 y = 6

Rewrite

4 x^{2} + 2 x + y^{2} - 10 y = 6

in the form of the standard ellipse equation

\frac{( x - ( - \frac{1}{4} ) ) ^{2}}{( \frac{5 5}{4} ) ^{2}} + \frac{( y - 5 ) ^{2}}{( \frac{5 5}{2} ) ^{2}} = 1

Therefore ellipse properties are:

(h, k) = (- \frac{1}{4}, 5), a = \frac{5 5}{4}, b = \frac{5 5}{2}

b > a

therefore

b

is semi-major axis and

a

is semi-minor axis

Ellipse with center (h, k) = (- \frac{1}{4}, 5), b = \frac{5 5}{2}, a = \frac{5 5}{4}

2 y^{2} + x^{2} = 1

36 x^{2} + 4 y^{2} - 49 = 0

9 x^{2} + 4 y^{2} + 72 x - 8 y - 176 = 0

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

\frac{( x - 3 ) ^{2}}{12} + \frac{( y + 4 ) ^{2}}{36} = 1

What is 4x^2+2x+y^2-10y=6 ?
The solution to 4x^2+2x+y^2-10y=6 is Ellipse with (h,k)=(-1/4 ,5),a=(5sqrt(5))/4 ,b=(5sqrt(5))/2