What is ((y-4)^2)/9+((x-1)^2)/4 =1 ?

The solution to ((y-4)^2)/9+((x-1)^2)/4 =1 is Ellipse with (h,k)=(1,4),a=2,b=3

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((y-4)^2)/9+((x-1)^2)/4 =1

\frac{( y - 4 ) ^{2}}{9} + \frac{( x - 1 ) ^{2}}{4} = 1

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

Solution steps

\frac{( y - 4 ) ^{2}}{9} + \frac{( x - 1 ) ^{2}}{4} = 1

Rewrite

\frac{( y - 4 ) ^{2}}{9} + \frac{( x - 1 ) ^{2}}{4} = 1

in the form of the standard ellipse equation

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

Therefore ellipse properties are:

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

b > a

therefore

b

is semi-major axis and

a

is semi-minor axis

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

\frac{x ^{2}}{85} + \frac{y ^{2}}{4} = 1

x, \frac{x ^{2}}{16} + \frac{Y ( x ) ^{2}}{4} = 1

\frac{x ^{2} - 2 x + y ^{2}}{4 - y} = 14

X^{2} + 2 Y^{2} - 2 X - 4 Y - 8 = 0

4 - x^{2} - 2 y^{2} = 0

What is ((y-4)^2)/9+((x-1)^2)/4 =1 ?
The solution to ((y-4)^2)/9+((x-1)^2)/4 =1 is Ellipse with (h,k)=(1,4),a=2,b=3