What is 4X^2+9Y^2-32X-36Y+64=0 ?

The solution to 4X^2+9Y^2-32X-36Y+64=0 is Ellipse with (h,k)=(4,2),a=3,b=2

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4X^2+9Y^2-32X-36Y+64=0

4 X^{2} + 9 Y^{2} - 32 X - 36 Y + 64 = 0

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

Solution steps

4 X^{2} + 9 Y^{2} - 32 X - 36 Y + 64 = 0

Rewrite

4 X^{2} + 9 Y^{2} - 32 X - 36 Y + 64 = 0

in the form of the standard ellipse equation

\frac{( X - 4 ) ^{2}}{3 ^{2}} + \frac{( Y - 2 ) ^{2}}{2 ^{2}} = 1

Therefore ellipse properties are:

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

a > b

therefore

a

is semi-major axis and

b

is semi-minor axis

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

What is 4X^2+9Y^2-32X-36Y+64=0 ?
The solution to 4X^2+9Y^2-32X-36Y+64=0 is Ellipse with (h,k)=(4,2),a=3,b=2