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

The solution to (x^2)/4+((y-1)^2)/9 <1 is Ellipse with (h,k)=(0,1),a=2,b=3

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

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

(h, k) = (0, 1), a = 2, b = 3

Solution steps

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

Rewrite

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

in the form of the standard ellipse equation

\frac{( x - 0 ) ^{2}}{2 ^{2}} + \frac{( y - 1 ) ^{2}}{3 ^{2}} = 1

Therefore ellipse properties are:

(h, k) = (0, 1), a = 2, b = 3

b > a

therefore

b

is semi-major axis and

a

is semi-minor axis

Ellipse with center (h, k) = (0, 1), b = 3, a = 2

\frac{( x + 2 ) ^{2}}{9} + \frac{( y - 3 ) ^{2}}{5} = 1

4 x^{2} + 25 y^{2} - 24 x + 250 y + 561 = 0

x^{2} + 9 y^{2} - 18 y = 0

100 x^{2} + 64 y^{2} = 1600

\frac{x ^{2}}{1} + \frac{y ^{2}}{9} = 1

What is (x^2)/4+((y-1)^2)/9 <1 ?
The solution to (x^2)/4+((y-1)^2)/9 <1 is Ellipse with (h,k)=(0,1),a=2,b=3