What is (25x^2)/(400-12^2)+(16y^2)/(400-12^2)=1 ?

The solution to (25x^2)/(400-12^2)+(16y^2)/(400-12^2)=1 is Ellipse with (h,k)=(0,0),a= 16/5 ,b=4

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(25x^2)/(400-12^2)+(16y^2)/(400-12^2)=1

\frac{25 x ^{2}}{400 - 1 2 ^{2}} + \frac{16 y ^{2}}{400 - 1 2 ^{2}} = 1

(h, k) = (0, 0), a = \frac{16}{5}, b = 4

Solution steps

\frac{25 x ^{2}}{400 - 1 2 ^{2}} + \frac{16 y ^{2}}{400 - 1 2 ^{2}} = 1

Rewrite

\frac{25 x ^{2}}{400 - 1 2 ^{2}} + \frac{16 y ^{2}}{400 - 1 2 ^{2}} = 1

in the form of the standard ellipse equation

\frac{( x - 0 ) ^{2}}{( \frac{16}{5} ) ^{2}} + \frac{( y - 0 ) ^{2}}{4 ^{2}} = 1

Therefore ellipse properties are:

(h, k) = (0, 0), a = \frac{16}{5}, b = 4

b > a

therefore

b

is semi-major axis and

a

is semi-minor axis

Ellipse with center (h, k) = (0, 0), b = 4, a = \frac{16}{5}

What is (25x^2)/(400-12^2)+(16y^2)/(400-12^2)=1 ?
The solution to (25x^2)/(400-12^2)+(16y^2)/(400-12^2)=1 is Ellipse with (h,k)=(0,0),a= 16/5 ,b=4