What is (x^2)/(a^2)+(y^2)/(b^2)<= 1 ?

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

Popular >

(x^2)/(a^2)+(y^2)/(b^2)<= 1

\frac{x ^{2}}{a ^{2}} + \frac{y ^{2}}{b ^{2}} \leq 1

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

Solution steps

\frac{x ^{2}}{a ^{2}} + \frac{y ^{2}}{b ^{2}} \leq 1

Rewrite

\frac{x ^{2}}{a ^{2}} + \frac{y ^{2}}{b ^{2}} \leq 1

in the form of the standard ellipse equation

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

Therefore ellipse properties are:

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

a > b

therefore

a

is semi-major axis and

b

is semi-minor axis

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

x^{2} - 4 x + 4 y^{2} + 8 y + 4 = 0

\frac{y ^{2}}{16} + \frac{( x + 1 ) ^{2}}{9} = 1

3 x^{2} + 5 y^{2} = 15

\frac{( x - 1 ) ^{2}}{36} + \frac{( y + 1 ) ^{2}}{25} = 1

8 x^{2} + 9 y^{2} - 16 x - 18 y - 55 = 0

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