What is 2(x^2+y^2)=x^2+(y-5/2)^2-25/4 ?

The solution to 2(x^2+y^2)=x^2+(y-5/2)^2-25/4 is Ellipse with (h,k)=(0,-5/2),a= 5/2 ,b= 5/2

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2(x^2+y^2)=x^2+(y-5/2)^2-25/4

2 (x^{2} + y^{2}) = x^{2} + (y - \frac{5}{2})^{2} - \frac{25}{4}

(h, k) = (0, - \frac{5}{2}), a = \frac{5}{2}, b = \frac{5}{2}

Solution steps

2 (x^{2} + y^{2}) = x^{2} + (y - \frac{5}{2})^{2} - \frac{25}{4}

Rewrite

2 (x^{2} + y^{2}) - x^{2} - (y - \frac{5}{2})^{2} + \frac{25}{4} = 0

in the form of the standard ellipse equation

\frac{( x - 0 ) ^{2}}{( \frac{5}{2} ) ^{2}} + \frac{( y - ( - \frac{5}{2} ) ) ^{2}}{( \frac{5}{2} ) ^{2}} = 1

Therefore ellipse properties are:

(h, k) = (0, - \frac{5}{2}), a = \frac{5}{2}, b = \frac{5}{2}

b > a

therefore

b

is semi-major axis and

a

is semi-minor axis

Ellipse with center (h, k) = (0, - \frac{5}{2}), b = \frac{5}{2}, a = \frac{5}{2}

- x^{2} - 9 y^{2} - 63 = 0

2 x^{2} + 3 y^{2} + 4 x - 1 = 0

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

16 x^{2} + 16 y^{2} - 8 y^{2} - 15 = 0

x^{(2)} + 4 y^{(2)} + 7 = 12 y - 2 x

What is 2(x^2+y^2)=x^2+(y-5/2)^2-25/4 ?
The solution to 2(x^2+y^2)=x^2+(y-5/2)^2-25/4 is Ellipse with (h,k)=(0,-5/2),a= 5/2 ,b= 5/2