What is 4x^2+y^2-8x+6y+9=0 ?

The solution to 4x^2+y^2-8x+6y+9=0 is Ellipse with (h,k)=(1,-3),a=1,b=2

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4x^2+y^2-8x+6y+9=0

4 x^{2} + y^{2} - 8 x + 6 y + 9 = 0

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

Solution steps

4 x^{2} + y^{2} - 8 x + 6 y + 9 = 0

Rewrite

4 x^{2} + y^{2} - 8 x + 6 y + 9 = 0

in the form of the standard ellipse equation

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

Therefore ellipse properties are:

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

b > a

therefore

b

is semi-major axis and

a

is semi-minor axis

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

\frac{( x + 3 ) ^{2}}{24} + \frac{( y - 5 ) ^{2}}{49} = 1

\frac{( x + 3 ) ^{2}}{64} + \frac{( y - 6 ) ^{2}}{100} = 1

y^{2} = 1 - 0.25 x^{2}

16 - x^{2} - 9 y^{2} = 0

256 x^{2} - 800 x + 625 = 400 x^{2} - 800 x + 400 y^{2} + 400

What is 4x^2+y^2-8x+6y+9=0 ?
The solution to 4x^2+y^2-8x+6y+9=0 is Ellipse with (h,k)=(1,-3),a=1,b=2