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

(5 p + 3 q) 2 = 25 p^{2} + 9 q^{2}

25 x^{2} + 9 y^{2} + 100 x + 36 y - 89 = 0

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

\frac{( x - 12 ) ^{2}}{100} + \frac{( y + 7 ) ^{2}}{36} = 1

12 x^{2} + 10 y^{2} = 120

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