What is 25x^2+16y^2=1 ?

The solution to 25x^2+16y^2=1 is Ellipse with (h,k)=(0,0),a= 1/5 ,b= 1/4

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25x^2+16y^2=1

25 x^{2} + 16 y^{2} = 1

(h, k) = (0, 0), a = \frac{1}{5}, b = \frac{1}{4}

Solution steps

25 x^{2} + 16 y^{2} = 1

Rewrite

25 x^{2} + 16 y^{2} = 1

in the form of the standard ellipse equation

\frac{( x - 0 ) ^{2}}{( \frac{1}{5} ) ^{2}} + \frac{( y - 0 ) ^{2}}{( \frac{1}{4} ) ^{2}} = 1

Therefore ellipse properties are:

(h, k) = (0, 0), a = \frac{1}{5}, b = \frac{1}{4}

b > a

therefore

b

is semi-major axis and

a

is semi-minor axis

Ellipse with center (h, k) = (0, 0), b = \frac{1}{4}, a = \frac{1}{5}

3 x^{2} + 7 y^{2} = 63

4 x^{2} + 32 x + 9 y^{2} + 36 y + 64 = 0

\frac{x ^{2}}{9} + \frac{( y + 5 ) ^{2}}{25} = 1

\frac{( x - 2 ) ^{2}}{9} + \frac{( y + 3 ) ^{2}}{10} = 1

\frac{x ^{2}}{16} + \frac{y ^{2}}{64} = 1

What is 25x^2+16y^2=1 ?
The solution to 25x^2+16y^2=1 is Ellipse with (h,k)=(0,0),a= 1/5 ,b= 1/4