What is (X^2)/(16)+(y-4)^2=1 ?

The solution to (X^2)/(16)+(y-4)^2=1 is Ellipse with (h,k)=(0,4),a=4,b=1

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(X^2)/(16)+(y-4)^2=1

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

(h, k) = (0, 4), a = 4, b = 1

Solution steps

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

Rewrite

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

in the form of the standard ellipse equation

\frac{( X - 0 ) ^{2}}{4 ^{2}} + \frac{( y - 4 ) ^{2}}{1 ^{2}} = 1

Therefore ellipse properties are:

(h, k) = (0, 4), a = 4, b = 1

a > b

therefore

a

is semi-major axis and

b

is semi-minor axis

Ellipse with center (h, k) = (0, 4), a = 4, b = 1

\frac{x ^{2}}{2 0 ^{2}} + \frac{y ^{2}}{1 5 ^{2}} = 1

25 x^{2} + 16 y^{2} - 100 x - 300 = 0

4 x^{2} + 24 x + 25 y^{2} - 300 y + 836 = 0

12 x^{2} = 336 - 7 y^{2}

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

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