What is (x^2+y^2)/(x^2+(y+1)^2)=16 ?

The solution to (x^2+y^2)/(x^2+(y+1)^2)=16 is Ellipse with (h,k)=(0,-16/15),a= 4/15 ,b= 4/15

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(x^2+y^2)/(x^2+(y+1)^2)=16

\frac{x ^{2} + y ^{2}}{x ^{2} + ( y + 1 ) ^{2}} = 16

(h, k) = (0, - \frac{16}{15}), a = \frac{4}{15}, b = \frac{4}{15}

Solution steps

\frac{x ^{2} + y ^{2}}{x ^{2} + ( y + 1 ) ^{2}} = 16

Rewrite

\frac{x ^{2} + y ^{2}}{x ^{2} + ( y + 1 ) ^{2}} = 16

in the form of the standard ellipse equation

\frac{( x - 0 ) ^{2}}{( \frac{4}{15} ) ^{2}} + \frac{( y - ( - \frac{16}{15} ) ) ^{2}}{( \frac{4}{15} ) ^{2}} = 1

Therefore ellipse properties are:

(h, k) = (0, - \frac{16}{15}), a = \frac{4}{15}, b = \frac{4}{15}

b > a

therefore

b

is semi-major axis and

a

is semi-minor axis

Ellipse with center (h, k) = (0, - \frac{16}{15}), b = \frac{4}{15}, a = \frac{4}{15}

200 = \frac{1000}{1 + x ^{2} + y ^{2}}

\frac{( x - 8 ) ^{2}}{42} + \frac{( y + 7 ) ^{2}}{16} = 1

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

6 x^{2} + 9 y^{2} + 54 y = 60 x - 87

16 x^{2} + 16 y^{2} = 1 + 2 x + x^{2}

What is (x^2+y^2)/(x^2+(y+1)^2)=16 ?
The solution to (x^2+y^2)/(x^2+(y+1)^2)=16 is Ellipse with (h,k)=(0,-16/15),a= 4/15 ,b= 4/15