What is 4x^2+9y^2=40 ?

The solution to 4x^2+9y^2=40 is Ellipse with (h,k)=(0,0),a=sqrt(10),b=(2sqrt(10))/3

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4x^2+9y^2=40

4 x^{2} + 9 y^{2} = 40

(h, k) = (0, 0), a = 10, b = \frac{2 10}{3}

Solution steps

4 x^{2} + 9 y^{2} = 40

Rewrite

4 x^{2} + 9 y^{2} = 40

in the form of the standard ellipse equation

\frac{( x - 0 ) ^{2}}{( 10 ) ^{2}} + \frac{( y - 0 ) ^{2}}{( \frac{2 10}{3} ) ^{2}} = 1

Therefore ellipse properties are:

(h, k) = (0, 0), a = 10, b = \frac{2 10}{3}

a > b

therefore

a

is semi-major axis and

b

is semi-minor axis

Ellipse with center (h, k) = (0, 0), a = 10, b = \frac{2 10}{3}

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

7 x^{2} + 16 y^{2} - 28 x - 128 y + 172 = 0

x^{2} + 5 y^{2} + 6 x - 40 y - 167 = 0

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

4 x^{2} + 9 y^{2} + 8 x - 36 y + 4 = 0

What is 4x^2+9y^2=40 ?
The solution to 4x^2+9y^2=40 is Ellipse with (h,k)=(0,0),a=sqrt(10),b=(2sqrt(10))/3