What is x^2+4y^2-20x+84=0 ?

The solution to x^2+4y^2-20x+84=0 is Ellipse with (h,k)=(10,0),a=4,b=2

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x^2+4y^2-20x+84=0

x^{2} + 4 y^{2} - 20 x + 84 = 0

(h, k) = (10, 0), a = 4, b = 2

Solution steps

x^{2} + 4 y^{2} - 20 x + 84 = 0

Rewrite

x^{2} + 4 y^{2} - 20 x + 84 = 0

in the form of the standard ellipse equation

\frac{( x - 10 ) ^{2}}{4 ^{2}} + \frac{( y - 0 ) ^{2}}{2 ^{2}} = 1

Therefore ellipse properties are:

(h, k) = (10, 0), a = 4, b = 2

a > b

therefore

a

is semi-major axis and

b

is semi-minor axis

Ellipse with center (h, k) = (10, 0), a = 4, b = 2

(x^{2} + y^{2} - 16 x + 8 y + 80) = 4 (x^{2} + y^{2} - 4 x - 8 y + 20)

16 (x - 2)^{2} + 25 (y + 3)^{2} = 124

3 x^{2} + y^{2} + 12 x - 2 y + 1 = 0

10 y^{2} + x^{2} = 5

9 x^{2} + 4 (y - 2)^{2} = 36

What is x^2+4y^2-20x+84=0 ?
The solution to x^2+4y^2-20x+84=0 is Ellipse with (h,k)=(10,0),a=4,b=2