What is 3x^2+2y^2=35 ?

The solution to 3x^2+2y^2=35 is Ellipse with (h,k)=(0,0),a=sqrt(35/3),b=sqrt(35/2)

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3x^2+2y^2=35

3 x^{2} + 2 y^{2} = 35

(h, k) = (0, 0), a = \frac{35}{3}, b = \frac{35}{2}

Solution steps

3 x^{2} + 2 y^{2} = 35

Rewrite

3 x^{2} + 2 y^{2} = 35

in the form of the standard ellipse equation

\frac{( x - 0 ) ^{2}}{( \frac{35}{3} ) ^{2}} + \frac{( y - 0 ) ^{2}}{( \frac{35}{2} ) ^{2}} = 1

Therefore ellipse properties are:

(h, k) = (0, 0), a = \frac{35}{3}, b = \frac{35}{2}

b > a

therefore

b

is semi-major axis and

a

is semi-minor axis

Ellipse with center (h, k) = (0, 0), b = \frac{35}{2}, a = \frac{35}{3}

x^{2} + 5 y^{2} - 4 x - 16 = 0

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

9 x^{2} + 25 y^{2} - 36 x - 50 y + 52 = 0

64 x^{2} + 81 y^{2} = 5184

x^{2} + 4 y^{2} - 2 x + 4 y + 1 = 0

What is 3x^2+2y^2=35 ?
The solution to 3x^2+2y^2=35 is Ellipse with (h,k)=(0,0),a=sqrt(35/3),b=sqrt(35/2)