What is (4x^2)/(25)+(9y^2)/(25)=1 ?

The solution to (4x^2)/(25)+(9y^2)/(25)=1 is Ellipse with (h,k)=(0,0),a= 5/2 ,b= 5/3

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(4x^2)/(25)+(9y^2)/(25)=1

\frac{4 x ^{2}}{25} + \frac{9 y ^{2}}{25} = 1

(h, k) = (0, 0), a = \frac{5}{2}, b = \frac{5}{3}

Solution steps

\frac{4 x ^{2}}{25} + \frac{9 y ^{2}}{25} = 1

Rewrite

\frac{4 x ^{2}}{25} + \frac{9 y ^{2}}{25} = 1

in the form of the standard ellipse equation

\frac{( x - 0 ) ^{2}}{( \frac{5}{2} ) ^{2}} + \frac{( y - 0 ) ^{2}}{( \frac{5}{3} ) ^{2}} = 1

Therefore ellipse properties are:

(h, k) = (0, 0), a = \frac{5}{2}, b = \frac{5}{3}

a > b

therefore

a

is semi-major axis and

b

is semi-minor axis

Ellipse with center (h, k) = (0, 0), a = \frac{5}{2}, b = \frac{5}{3}

X^{2} + 8 Y^{2} - 5 = 0

\frac{( x - 2 ) ^{2}}{12} + \frac{( y + 5 ) ^{2}}{8} = 1

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

4 (x - 3)^{2} + 2 y^{2} = 8

9 x^{2} + 36 y^{2} + 18 x - 360 y + 585 = 0

What is (4x^2)/(25)+(9y^2)/(25)=1 ?
The solution to (4x^2)/(25)+(9y^2)/(25)=1 is Ellipse with (h,k)=(0,0),a= 5/2 ,b= 5/3