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

The solution to (x^2+y^2)/x =16 is Ellipse with (h,k)=(8,0),a=8,b=8

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

\frac{x ^{2} + y ^{2}}{x} = 16

(h, k) = (8, 0), a = 8, b = 8

Solution steps

\frac{x ^{2} + y ^{2}}{x} = 16

Rewrite

\frac{x ^{2} + y ^{2}}{x} = 16

in the form of the standard ellipse equation

\frac{( x - 8 ) ^{2}}{8 ^{2}} + \frac{( y - 0 ) ^{2}}{8 ^{2}} = 1

Therefore ellipse properties are:

(h, k) = (8, 0), a = 8, b = 8

b > a

therefore

b

is semi-major axis and

a

is semi-minor axis

Ellipse with center (h, k) = (8, 0), b = 8, a = 8

4 x^{(2)} + 16 y^{(2)} - 16 x - 48 = 0

\frac{( x ^{2} )}{( 16 )} + \frac{( y ^{2} )}{( 12 )} = 1

\frac{( x - 3 ) ^{2}}{16} + \frac{( y - 7 ) ^{2}}{64} = 1

2 x^{2} + 3 y^{2} + 4 x = 19

x^{2} + 6 x + (5 y + 6)^{2} - 2 (5 y + 6) + 10 = 4

What is (x^2+y^2)/x =16 ?
The solution to (x^2+y^2)/x =16 is Ellipse with (h,k)=(8,0),a=8,b=8