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

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

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x^2+49y^2=49

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

(h, k) = (0, 0), a = 7, b = 1

Solution steps

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

Rewrite

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

in the form of the standard ellipse equation

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

Therefore ellipse properties are:

(h, k) = (0, 0), a = 7, b = 1

a > b

therefore

a

is semi-major axis and

b

is semi-minor axis

Ellipse with center (h, k) = (0, 0), a = 7, b = 1

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

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

\frac{x ^{2}}{25} + \frac{y ^{2}}{49} = 1

\frac{x ^{2}}{15} + \frac{y ^{2}}{17} = 1

4 x^{2} + y^{2} + 40 x + 6 y + 95 = 0

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