What is (x^2)/4+(y^2)/(25)-1>= 0 ?

The solution to (x^2)/4+(y^2)/(25)-1>= 0 is Ellipse with (h,k)=(0,0),a=2,b=5

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(x^2)/4+(y^2)/(25)-1>= 0

\frac{x ^{2}}{4} + \frac{y ^{2}}{25} - 1 \geq 0

(h, k) = (0, 0), a = 2, b = 5

Solution steps

\frac{x ^{2}}{4} + \frac{y ^{2}}{25} - 1 \geq 0

Rewrite

\frac{x ^{2}}{4} + \frac{y ^{2}}{25} - 1 \geq 0

in the form of the standard ellipse equation

\frac{( x - 0 ) ^{2}}{2 ^{2}} + \frac{( y - 0 ) ^{2}}{5 ^{2}} = 1

Therefore ellipse properties are:

(h, k) = (0, 0), a = 2, b = 5

b > a

therefore

b

is semi-major axis and

a

is semi-minor axis

Ellipse with center (h, k) = (0, 0), b = 5, a = 2

\frac{( x + 3 ) ^{2}}{3 ^{2}} + \frac{( y - 6 ) ^{2}}{6 ^{2}} = 1

\frac{x ^{2}}{4} + \frac{y ^{2}}{84} = 1

25 x^{2} + 9 y^{2} - 100 x + 18 y - 118 = 0

\frac{( x - 5 ) ^{2}}{64} + \frac{y ^{2}}{89} = 1

2 x^{2} + 6 y^{2} = 12

What is (x^2)/4+(y^2)/(25)-1>= 0 ?
The solution to (x^2)/4+(y^2)/(25)-1>= 0 is Ellipse with (h,k)=(0,0),a=2,b=5