What is 7x^2+9y^2=1 ?

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

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7x^2+9y^2=1

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

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

Solution steps

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

Rewrite

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

in the form of the standard ellipse equation

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

Therefore ellipse properties are:

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

a > b

therefore

a

is semi-major axis and

b

is semi-minor axis

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

\frac{x ^{2}}{2.3 2 ^{2}} + \frac{y ^{2}}{2.8 2 ^{2}} = 1

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

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

- 8 y^{2} + 72 = 9 x^{2}

\frac{( x + 3 ) ^{2}}{36} + \frac{( y - 4 ) ^{2}}{16} = 1

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