What is 4x^2+3y^2=1 ?

The solution to 4x^2+3y^2=1 is Ellipse with (h,k)=(0,0),a= 1/2 ,b=sqrt(1/3)

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4x^2+3y^2=1

4 x^{2} + 3 y^{2} = 1

(h, k) = (0, 0), a = \frac{1}{2}, b = \frac{1}{3}

Solution steps

4 x^{2} + 3 y^{2} = 1

Rewrite

4 x^{2} + 3 y^{2} = 1

in the form of the standard ellipse equation

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

Therefore ellipse properties are:

(h, k) = (0, 0), a = \frac{1}{2}, b = \frac{1}{3}

b > a

therefore

b

is semi-major axis and

a

is semi-minor axis

Ellipse with center (h, k) = (0, 0), b = \frac{1}{3}, a = \frac{1}{2}

4 x^{2} + y^{2} = 8

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

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

\frac{( x + 0 ) ^{2}}{\frac{225}{25}} + \frac{( y - 1 ) ^{2}}{\frac{225}{9}} = 1

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

What is 4x^2+3y^2=1 ?
The solution to 4x^2+3y^2=1 is Ellipse with (h,k)=(0,0),a= 1/2 ,b=sqrt(1/3)