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

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

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

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

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

Solution steps

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

Rewrite

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

in the form of the standard ellipse equation

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

Therefore ellipse properties are:

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

a > b

therefore

a

is semi-major axis and

b

is semi-minor axis

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

(x - 2)^{2} + (2 y + 3)^{2} = 26

144 = 4 x^{2} + y^{2}

9 x^{2} + 18 x + 16 y^{2} - 64 y - 71 = 0

16 x^{2} + 36 y^{2} - 96 x + 144 y + 144 = 0

9 x^{2} + 36 x + 16 y^{2} - 96 y = - 36

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