What is (x-5)^2+(y-1)^2+(y-1)^2=14 ?

The solution to (x-5)^2+(y-1)^2+(y-1)^2=14 is Ellipse with (h,k)=(5,1),a=sqrt(14),b=sqrt(7)

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(x-5)^2+(y-1)^2+(y-1)^2=14

(x - 5)^{2} + (y - 1)^{2} + (y - 1)^{2} = 14

(h, k) = (5, 1), a = 14, b = 7

Solution steps

(x - 5)^{2} + (y - 1)^{2} + (y - 1)^{2} = 14

Rewrite

(x - 5)^{2} + (y - 1)^{2} + (y - 1)^{2} = 14

in the form of the standard ellipse equation

\frac{( x - 5 ) ^{2}}{( 14 ) ^{2}} + \frac{( y - 1 ) ^{2}}{( 7 ) ^{2}} = 1

Therefore ellipse properties are:

(h, k) = (5, 1), a = 14, b = 7

a > b

therefore

a

is semi-major axis and

b

is semi-minor axis

Ellipse with center (h, k) = (5, 1), a = 14, b = 7

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

\frac{( x - 3 ) ^{2}}{( 18 )} + \frac{( y + 1 ) ^{2}}{12} = 1

4 x^{2} + 8 y^{2} - 16 \cdot + 32 y + 32 = 0

\frac{x ^{2}}{6} + \frac{y ^{2}}{2} = 1

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

What is (x-5)^2+(y-1)^2+(y-1)^2=14 ?
The solution to (x-5)^2+(y-1)^2+(y-1)^2=14 is Ellipse with (h,k)=(5,1),a=sqrt(14),b=sqrt(7)