What is 16x^2+25y^2=1400 ?

The solution to 16x^2+25y^2=1400 is Ellipse with (h,k)=(0,0),a=(5sqrt(7))/(sqrt(2)),b=2sqrt(14)

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16x^2+25y^2=1400

16 x^{2} + 25 y^{2} = 1400

(h, k) = (0, 0), a = \frac{5 7}{2}, b = 214

Solution steps

16 x^{2} + 25 y^{2} = 1400

Rewrite

16 x^{2} + 25 y^{2} = 1400

in the form of the standard ellipse equation

\frac{( x - 0 ) ^{2}}{( \frac{5 7}{2} ) ^{2}} + \frac{( y - 0 ) ^{2}}{( 2 14 ) ^{2}} = 1

Therefore ellipse properties are:

(h, k) = (0, 0), a = \frac{5 7}{2}, b = 214

a > b

therefore

a

is semi-major axis and

b

is semi-minor axis

Ellipse with center (h, k) = (0, 0), a = \frac{5 7}{2}, b = 214

5 x^{2} + 9 y^{2} - 80 x + 54 y + 221 = 0

(\frac{x}{16})^{2} + \frac{y ^{2}}{81} = 1

11 x^{2} + 5 y^{2} + 110 x - 20 y + 240 = 0

\frac{x ^{2}}{cosh ^{2} ( β )} + \frac{y ^{2}}{sinh ^{2} ( β )} = 1

4 x^{2} = 36 - 9 y^{2}

What is 16x^2+25y^2=1400 ?
The solution to 16x^2+25y^2=1400 is Ellipse with (h,k)=(0,0),a=(5sqrt(7))/(sqrt(2)),b=2sqrt(14)