What is (x^2-2x+y^2)/(4-y)=14 ?

The solution to (x^2-2x+y^2)/(4-y)=14 is Ellipse with (h,k)=(1,-7),a=sqrt(106),b=sqrt(106)

Popular >

(x^2-2x+y^2)/(4-y)=14

\frac{x ^{2} - 2 x + y ^{2}}{4 - y} = 14

(h, k) = (1, - 7), a = 106, b = 106

Solution steps

\frac{x ^{2} - 2 x + y ^{2}}{4 - y} = 14

Rewrite

\frac{x ^{2} - 2 x + y ^{2}}{4 - y} = 14

in the form of the standard ellipse equation

\frac{( x - 1 ) ^{2}}{( 106 ) ^{2}} + \frac{( y - ( - 7 ) ) ^{2}}{( 106 ) ^{2}} = 1

Therefore ellipse properties are:

(h, k) = (1, - 7), a = 106, b = 106

b > a

therefore

b

is semi-major axis and

a

is semi-minor axis

Ellipse with center (h, k) = (1, - 7), b = 106, a = 106

X^{2} + 2 Y^{2} - 2 X - 4 Y - 8 = 0

4 - x^{2} - 2 y^{2} = 0

4 x^{2} + 9 y^{2} - 8 x + 36 y - 104 = 0

\frac{( y - 3 ) ^{2}}{9} + \frac{( x - 2 ) ^{2}}{2} = 1

4 X^{2} + 6 Y^{2} - 24 X + 2 Y - 12 = 0

What is (x^2-2x+y^2)/(4-y)=14 ?
The solution to (x^2-2x+y^2)/(4-y)=14 is Ellipse with (h,k)=(1,-7),a=sqrt(106),b=sqrt(106)