What is 4x^2+9y^2-16x-36y+16=0 ?

The solution to 4x^2+9y^2-16x-36y+16=0 is Ellipse with (h,k)=(2,2),a=3,b=2

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4x^2+9y^2-16x-36y+16=0

4 x^{2} + 9 y^{2} - 16 x - 36 y + 16 = 0

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

Solution steps

4 x^{2} + 9 y^{2} - 16 x - 36 y + 16 = 0

Rewrite

4 x^{2} + 9 y^{2} - 16 x - 36 y + 16 = 0

in the form of the standard ellipse equation

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

Therefore ellipse properties are:

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

a > b

therefore

a

is semi-major axis and

b

is semi-minor axis

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

\frac{( x + 2 ) ^{2}}{36} + \frac{( y + 1 ) ^{2}}{25} = 1

4 x^{2} + 7 y^{2} = 1

\frac{( x - 3 ) ^{2}}{16} + \frac{( y - 1 ) ^{2}}{4} = 1

4 x^{2} + y^{2} - 32 x + 16 y + 124 = 0

3 x^{2} + 2 y^{2} = 11

What is 4x^2+9y^2-16x-36y+16=0 ?
The solution to 4x^2+9y^2-16x-36y+16=0 is Ellipse with (h,k)=(2,2),a=3,b=2