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)

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(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

10 x^{2} + 6 y^{2} - 60 = 0

9 y^{2} + x^{2} = 81

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

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

\frac{( x ^{2} )}{9} + \frac{( ( y - 1 ) ^{2} )}{25} = 1

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)