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

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

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

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

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

Solution steps

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

Rewrite

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

in the form of the standard ellipse equation

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

Therefore ellipse properties are:

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

b > a

therefore

b

is semi-major axis and

a

is semi-minor axis

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

1 - (x^{2} + y^{2}) = x^{2} + (y - 1)^{2}

\frac{x ^{2}}{36} + \frac{y ^{2}}{20} = 1

\frac{x ^{2}}{4} + \frac{y ^{2}}{7} = 1

16 x^{2} + 9 y^{2} + 160 x - 72 y + 544 = 144

\frac{( x - 2 ) ^{2}}{9} + \frac{( y + 3 ) ^{2}}{4} = 1

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