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

The solution to -4y^2-6y=x^2 is Ellipse with (h,k)=(0,-3/4),a= 3/2 ,b= 3/4

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

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

(h, k) = (0, - \frac{3}{4}), a = \frac{3}{2}, b = \frac{3}{4}

Solution steps

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

Rewrite

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

in the form of the standard ellipse equation

\frac{( x - 0 ) ^{2}}{( \frac{3}{2} ) ^{2}} + \frac{( y - ( - \frac{3}{4} ) ) ^{2}}{( \frac{3}{4} ) ^{2}} = 1

Therefore ellipse properties are:

(h, k) = (0, - \frac{3}{4}), a = \frac{3}{2}, b = \frac{3}{4}

a > b

therefore

a

is semi-major axis and

b

is semi-minor axis

Ellipse with center (h, k) = (0, - \frac{3}{4}), a = \frac{3}{2}, b = \frac{3}{4}

7 x^{(2)} + 10 y^{(2)} - 56 x + 100 y + 292 = 0

\frac{x ^{2}}{17} + \frac{y ^{2}}{15} = 1

5 x^{2} + 7 y^{2} = 70

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

9 x^{2} + 25 y^{2} - 18 x - 250 y + 409 = 0

What is -4y^2-6y=x^2 ?
The solution to -4y^2-6y=x^2 is Ellipse with (h,k)=(0,-3/4),a= 3/2 ,b= 3/4