What is x^2+4y^2-10x+16y+37=0 ?

The solution to x^2+4y^2-10x+16y+37=0 is Ellipse with (h,k)=(5,-2),a=2,b=1

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x^2+4y^2-10x+16y+37=0

x^{2} + 4 y^{2} - 10 x + 16 y + 37 = 0

(h, k) = (5, - 2), a = 2, b = 1

Solution steps

x^{2} + 4 y^{2} - 10 x + 16 y + 37 = 0

Rewrite

x^{2} + 4 y^{2} - 10 x + 16 y + 37 = 0

in the form of the standard ellipse equation

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

Therefore ellipse properties are:

(h, k) = (5, - 2), a = 2, b = 1

a > b

therefore

a

is semi-major axis and

b

is semi-minor axis

Ellipse with center (h, k) = (5, - 2), a = 2, b = 1

9 y^{2} = 36 - x^{2}

9 x^{2} + 5 y^{2} + 36 x - 30 y + 36 = 0

x, 4 x^{2} = 20 x - p (x)^{2} + 4

3 x^{2} + 4 y^{2} - 12 x + 16 y + 16 = 0

3 x^{2} + 5 y^{2} + 6 x - 10 y + 7 = 0

What is x^2+4y^2-10x+16y+37=0 ?
The solution to x^2+4y^2-10x+16y+37=0 is Ellipse with (h,k)=(5,-2),a=2,b=1