What is 4x^2+3y^2=25 ?

The solution to 4x^2+3y^2=25 is Ellipse with (h,k)=(0,0),a= 5/2 ,b= 5/(sqrt(3))

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4x^2+3y^2=25

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

(h, k) = (0, 0), a = \frac{5}{2}, b = \frac{5}{3}

Solution steps

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

Rewrite

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

in the form of the standard ellipse equation

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

Therefore ellipse properties are:

(h, k) = (0, 0), a = \frac{5}{2}, b = \frac{5}{3}

b > a

therefore

b

is semi-major axis and

a

is semi-minor axis

Ellipse with center (h, k) = (0, 0), b = \frac{5}{3}, a = \frac{5}{2}

4 x^{2} + 3 y^{2} = 26

9 x^{2} + 8 y^{2} = 3

4 x^{2} + 3 y^{2} = 30

2 x^{2} + 8 y^{2} - 128 = 0

x^{2} + y^{2} = - y

What is 4x^2+3y^2=25 ?
The solution to 4x^2+3y^2=25 is Ellipse with (h,k)=(0,0),a= 5/2 ,b= 5/(sqrt(3))