What is x^2+16y^2-2x-64y+49=0 ?

The solution to x^2+16y^2-2x-64y+49=0 is Ellipse with (h,k)=(1,2),a=4,b=1

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x^2+16y^2-2x-64y+49=0

x^{2} + 16 y^{2} - 2 x - 64 y + 49 = 0

(h, k) = (1, 2), a = 4, b = 1

Solution steps

x^{2} + 16 y^{2} - 2 x - 64 y + 49 = 0

Rewrite

x^{2} + 16 y^{2} - 2 x - 64 y + 49 = 0

in the form of the standard ellipse equation

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

Therefore ellipse properties are:

(h, k) = (1, 2), a = 4, b = 1

a > b

therefore

a

is semi-major axis and

b

is semi-minor axis

Ellipse with center (h, k) = (1, 2), a = 4, b = 1

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

\frac{( x - 5 ) ^{2}}{2 ^{2}} + \frac{( y - 3 ) ^{2}}{9} = 1

25 x^{2} + 9 y^{2} + 100 x - 125 = 0

\frac{1}{x + i y} + \frac{1}{x - i y} < - 1

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

What is x^2+16y^2-2x-64y+49=0 ?
The solution to x^2+16y^2-2x-64y+49=0 is Ellipse with (h,k)=(1,2),a=4,b=1