What is y=(2x-4)/(-2y+4)x+6 ?

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

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y=(2x-4)/(-2y+4)x+6

y = \frac{2 x - 4}{- 2 y + 4} x + 6

(h, k) = (1, 4), a = 5, b = 5

Solution steps

y = \frac{2 x - 4}{- 2 y + 4} x + 6

Rewrite

y - \frac{2 x - 4}{- 2 y + 4} x - 6 = 0

in the form of the standard ellipse equation

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

Therefore ellipse properties are:

(h, k) = (1, 4), a = 5, b = 5

b > a

therefore

b

is semi-major axis and

a

is semi-minor axis

Ellipse with center (h, k) = (1, 4), b = 5, a = 5

x^{2} + 4 y^{2} + 9 x + 10 y - 14 = 0

\frac{( x + 1 ) ^{2}}{4} + \frac{( y - \frac{3}{2} ) ^{2}}{8} = 1

\frac{( x - 2 ) ^{2}}{4 ^{2}} + \frac{( y - 3 ) ^{2}}{5 ^{2}} = 1

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

y^{2} + \frac{5}{2} y + \frac{x ^{2}}{4} - 44 = 0

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