What is 3x^2+y^2=25 ?

The solution to 3x^2+y^2=25 is Ellipse with (h,k)=(0,0),a= 5/(sqrt(3)),b=5

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3x^2+y^2=25

3 x^{2} + y^{2} = 25

(h, k) = (0, 0), a = \frac{5}{3}, b = 5

Solution steps

3 x^{2} + y^{2} = 25

Rewrite

3 x^{2} + y^{2} = 25

in the form of the standard ellipse equation

\frac{( x - 0 ) ^{2}}{( \frac{5}{3} ) ^{2}} + \frac{( y - 0 ) ^{2}}{5 ^{2}} = 1

Therefore ellipse properties are:

(h, k) = (0, 0), a = \frac{5}{3}, b = 5

b > a

therefore

b

is semi-major axis and

a

is semi-minor axis

Ellipse with center (h, k) = (0, 0), b = 5, a = \frac{5}{3}

2 x^{2} + 9 y^{2} - 12 x - 18 y + 9 = 0

\frac{x ^{2}}{100} + \frac{y ^{2}}{144} = 1

3 x^{2} + 2 y^{2} - 17 x = 0

x^{2} + 4 y^{2} + 10 x + 24 y + 25 = 0

(x - 3)^{2} + 4 (y + 1)^{2} = 1

What is 3x^2+y^2=25 ?
The solution to 3x^2+y^2=25 is Ellipse with (h,k)=(0,0),a= 5/(sqrt(3)),b=5