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

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

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

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

(h, k) = (2, 2), a = 25, b = 25

Solution steps

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

Rewrite

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

in the form of the standard ellipse equation

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

Therefore ellipse properties are:

(h, k) = (2, 2), a = 25, b = 25

b > a

therefore

b

is semi-major axis and

a

is semi-minor axis

Ellipse with center (h, k) = (2, 2), b = 25, a = 25

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

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

- 25 x^{2} - 4 y^{2} = - 100

\frac{( x + 4 ) ^{2}}{49} + \frac{( y - 4 ) ^{2}}{25} = 1

y^{2} + \frac{x ^{2}}{4} = 1

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