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

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

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

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

(h, k) = (0, 0), a = \frac{1}{9}, b = \frac{1}{7}

Solution steps

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

Rewrite

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

in the form of the standard ellipse equation

\frac{( x - 0 ) ^{2}}{( \frac{1}{9} ) ^{2}} + \frac{( y - 0 ) ^{2}}{( \frac{1}{7} ) ^{2}} = 1

Therefore ellipse properties are:

(h, k) = (0, 0), a = \frac{1}{9}, b = \frac{1}{7}

b > a

therefore

b

is semi-major axis and

a

is semi-minor axis

Ellipse with center (h, k) = (0, 0), b = \frac{1}{7}, a = \frac{1}{9}

\frac{( x - 2 ) ^{2}}{9} + \frac{( y - 3 ) ^{2}}{5} = 1

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

16 x^{2} + 9 y^{2} - 128 x - 90 y + 337 = 0

(x + 6)^{2} + \frac{( y + 4 ) ^{2}}{\frac{1}{16}} = 1

4 (x - 1)^{2} + 9 y^{2} = 36

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