What is 4x^2+y^2-16x-6y+21=0 ?

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

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

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

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

Solution steps

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

Rewrite

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

in the form of the standard ellipse equation

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

Therefore ellipse properties are:

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

b > a

therefore

b

is semi-major axis and

a

is semi-minor axis

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

25 x^{2} + 16 y^{2} + 50 x - 64 y - 311 = 0

18 x^{2} + 24 x + 12 y^{2} - 12 y = 1

16 x^{2} + 25 y^{2} - 64 x - 50 y - 311 = 0

2 (x + 1)^{2} + (y - 2)^{2} = 25

2 x^{2} + y^{2} - 7 = 0

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