What is 5x^2+7y^2=35 ?

The solution to 5x^2+7y^2=35 is Ellipse with (h,k)=(0,0),a=sqrt(7),b=sqrt(5)

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5x^2+7y^2=35

5 x^{2} + 7 y^{2} = 35

(h, k) = (0, 0), a = 7, b = 5

Solution steps

5 x^{2} + 7 y^{2} = 35

Rewrite

5 x^{2} + 7 y^{2} = 35

in the form of the standard ellipse equation

\frac{( x - 0 ) ^{2}}{( 7 ) ^{2}} + \frac{( y - 0 ) ^{2}}{( 5 ) ^{2}} = 1

Therefore ellipse properties are:

(h, k) = (0, 0), a = 7, b = 5

a > b

therefore

a

is semi-major axis and

b

is semi-minor axis

Ellipse with center (h, k) = (0, 0), a = 7, b = 5

(\frac{x ^{2}}{a}) + (\frac{y ^{2}}{b}) = 1

\frac{( x - 10 ) ^{2}}{25} + \frac{( y - 4 ) ^{2}}{36} = 1

3 x^{2} + 2 y^{2} - 6 x + 4 y - 2 = 0

9 x^{(2)} + 25 y^{(2)} + 18 x + 150 y + 9 = 0

\frac{y ^{2}}{4} + \frac{x ^{2}}{9} = 1

What is 5x^2+7y^2=35 ?
The solution to 5x^2+7y^2=35 is Ellipse with (h,k)=(0,0),a=sqrt(7),b=sqrt(5)