What is 25x^2+9y^2-25=0 ?

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

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25x^2+9y^2-25=0

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

(h, k) = (0, 0), a = 1, b = \frac{5}{3}

Solution steps

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

Rewrite

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

in the form of the standard ellipse equation

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

Therefore ellipse properties are:

(h, k) = (0, 0), a = 1, b = \frac{5}{3}

b > a

therefore

b

is semi-major axis and

a

is semi-minor axis

Ellipse with center (h, k) = (0, 0), b = \frac{5}{3}, a = 1

y^{2} + \frac{5}{2} y + \frac{x ^{2}}{4} - 44 = 0

\frac{x ^{2}}{100} + \frac{y ^{2}}{52} = 1

\frac{( x - 14 ) ^{2}}{3} + \frac{( y - 11 ) ^{2}}{4} = 1

x^{2} + 7 y^{2} = 12

\frac{( x - 3 ) ^{2}}{64} + \frac{( y + 1 ) ^{2}}{25} = 1

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