What is 4x^2+y^2-16x+6y+9=0 ?

The solution to 4x^2+y^2-16x+6y+9=0 is Ellipse with (h,k)=(2,-3),a=2,b=4

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4x^2+y^2-16x+6y+9=0

4 x^{2} + y^{2} - 16 x + 6 y + 9 = 0

(h, k) = (2, - 3), a = 2, b = 4

Solution steps

4 x^{2} + y^{2} - 16 x + 6 y + 9 = 0

Rewrite

4 x^{2} + y^{2} - 16 x + 6 y + 9 = 0

in the form of the standard ellipse equation

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

Therefore ellipse properties are:

(h, k) = (2, - 3), a = 2, b = 4

b > a

therefore

b

is semi-major axis and

a

is semi-minor axis

Ellipse with center (h, k) = (2, - 3), b = 4, a = 2

x^{2} + 9 y^{2} = 18

9 x^{2} + 4 y^{2} - 18 x + 8 y = 23

1 x^{2} + 2 y^{2} = 9

\frac{( x - 3 ) ^{2}}{64} + \frac{( y - 3 ) ^{2}}{16} = 1

4 x^{2} + y^{2} + 48 x + 128 = 0

What is 4x^2+y^2-16x+6y+9=0 ?
The solution to 4x^2+y^2-16x+6y+9=0 is Ellipse with (h,k)=(2,-3),a=2,b=4