What is 4x^2+9y^2<= 36 ?

The solution to 4x^2+9y^2<= 36 is Ellipse with (h,k)=(0,0),a=3,b=2

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4x^2+9y^2<= 36

4 x^{2} + 9 y^{2} \leq 36

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

Solution steps

4 x^{2} + 9 y^{2} \leq 36

Rewrite

4 x^{2} + 9 y^{2} \leq 36

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} + 6 x + 9 + y^{2} = 28.09 + \frac{9 x ^{2}}{16}

\frac{( x + 2 ) ^{2}}{36} + \frac{( y - 3 ) ^{2}}{9} = 1

- x^{2} - \frac{y ^{2}}{4} = - 1

x^{2} + 4 y^{2} - 2 x + 16 y + 1 = 0

4 x^{2} + 2 y^{2} - 2 x + 4 y - 7 = 0

What is 4x^2+9y^2<= 36 ?
The solution to 4x^2+9y^2<= 36 is Ellipse with (h,k)=(0,0),a=3,b=2