What is (x-3)^2+16(y-2)^2=16 ?

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

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(x-3)^2+16(y-2)^2=16

(x - 3)^{2} + 16 (y - 2)^{2} = 16

(h, k) = (3, 2), a = 4, b = 1

Solution steps

(x - 3)^{2} + 16 (y - 2)^{2} = 16

Rewrite

(x - 3)^{2} + 16 (y - 2)^{2} = 16

in the form of the standard ellipse equation

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

Therefore ellipse properties are:

(h, k) = (3, 2), a = 4, b = 1

a > b

therefore

a

is semi-major axis and

b

is semi-minor axis

Ellipse with center (h, k) = (3, 2), a = 4, b = 1

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