What is 7x^2+5y^2=1 ?

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

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7x^2+5y^2=1

7 x^{2} + 5 y^{2} = 1

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

Solution steps

7 x^{2} + 5 y^{2} = 1

Rewrite

7 x^{2} + 5 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}{5} ) ^{2}} = 1

Therefore ellipse properties are:

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

b > a

therefore

b

is semi-major axis and

a

is semi-minor axis

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

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