What is x^{(2)}+4y^{(2)}-6x+16y+21=0 ?

The solution to x^{(2)}+4y^{(2)}-6x+16y+21=0 is Ellipse with (h,k)=(3,-2),a=2,b=1

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x^{(2)}+4y^{(2)}-6x+16y+21=0

x^{(2)} + 4 y^{(2)} - 6 x + 16 y + 21 = 0

(h, k) = (3, - 2), a = 2, b = 1

Solution steps

x^{2} + 4 y^{2} - 6 x + 16 y + 21 = 0

Rewrite

x^{2} + 4 y^{2} - 6 x + 16 y + 21 = 0

in the form of the standard ellipse equation

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

Therefore ellipse properties are:

(h, k) = (3, - 2), a = 2, b = 1

a > b

therefore

a

is semi-major axis and

b

is semi-minor axis

Ellipse with center (h, k) = (3, - 2), a = 2, b = 1

16 x^{2} + 25 y^{2} - 64 x - 336 = 0

x^{2} + 2 y^{2} - 4 y = 6

2 x^{2} + 4 y^{2} = 1

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

4 x^{2} + 9 y^{2} - 16 x - 54 y + 61 = 0

What is x^{(2)}+4y^{(2)}-6x+16y+21=0 ?
The solution to x^{(2)}+4y^{(2)}-6x+16y+21=0 is Ellipse with (h,k)=(3,-2),a=2,b=1