What is 25x^2+49y^2=49 ?

The solution to 25x^2+49y^2=49 is Ellipse with (h,k)=(0,0),a= 7/5 ,b=1

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25x^2+49y^2=49

25 x^{2} + 49 y^{2} = 49

(h, k) = (0, 0), a = \frac{7}{5}, b = 1

Solution steps

25 x^{2} + 49 y^{2} = 49

Rewrite

25 x^{2} + 49 y^{2} = 49

in the form of the standard ellipse equation

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

Therefore ellipse properties are:

(h, k) = (0, 0), a = \frac{7}{5}, b = 1

a > b

therefore

a

is semi-major axis and

b

is semi-minor axis

Ellipse with center (h, k) = (0, 0), a = \frac{7}{5}, b = 1

x^{2} + x + 2 y^{2} + y - 1 = 0

\frac{( x - 4 ) ^{2}}{5} + \frac{( y - 6 ) ^{2}}{9} = 1

(\frac{( x + 2 ) ^{2}}{25}) + (\frac{( y - 1 ) ^{2}}{169}) = 1

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

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

What is 25x^2+49y^2=49 ?
The solution to 25x^2+49y^2=49 is Ellipse with (h,k)=(0,0),a= 7/5 ,b=1