What is 9x^2+49y^2=1 ?

The solution to 9x^2+49y^2=1 is Ellipse with (h,k)=(0,0),a= 1/3 ,b= 1/7

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9x^2+49y^2=1

9 x^{2} + 49 y^{2} = 1

(h, k) = (0, 0), a = \frac{1}{3}, b = \frac{1}{7}

Solution steps

9 x^{2} + 49 y^{2} = 1

Rewrite

9 x^{2} + 49 y^{2} = 1

in the form of the standard ellipse equation

\frac{( x - 0 ) ^{2}}{( \frac{1}{3} ) ^{2}} + \frac{( y - 0 ) ^{2}}{( \frac{1}{7} ) ^{2}} = 1

Therefore ellipse properties are:

(h, k) = (0, 0), a = \frac{1}{3}, b = \frac{1}{7}

a > b

therefore

a

is semi-major axis and

b

is semi-minor axis

Ellipse with center (h, k) = (0, 0), a = \frac{1}{3}, b = \frac{1}{7}

8 x^{2} + 18 y^{2} + 32 x - 36 y - 22 = 0

4 x^{2} + 2 y^{2} = 19

10 x^{2} + y^{2} - 40 x = 0

4 x^{2} + 16 x + 16 y^{2} - 32 y - 32 = 0

\frac{( x ^{(2)} )}{( 16 )} + \frac{( y ^{(2)} )}{( 7 )} = 1

What is 9x^2+49y^2=1 ?
The solution to 9x^2+49y^2=1 is Ellipse with (h,k)=(0,0),a= 1/3 ,b= 1/7