What is 5x^2+3y^2-15=0 ?

The solution to 5x^2+3y^2-15=0 is Ellipse with (h,k)=(0,0),a=sqrt(3),b=sqrt(5)

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5x^2+3y^2-15=0

5 x^{2} + 3 y^{2} - 15 = 0

(h, k) = (0, 0), a = 3, b = 5

Solution steps

5 x^{2} + 3 y^{2} - 15 = 0

Rewrite

5 x^{2} + 3 y^{2} - 15 = 0

in the form of the standard ellipse equation

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

Therefore ellipse properties are:

(h, k) = (0, 0), a = 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 = 3

\frac{y ^{2}}{b ^{2}} = 1 - \frac{x ^{2}}{a ^{2}}

- 1 (- 4 x^{2} - y^{2} + 16) \geq - 1 (0)

\frac{x ^{2}}{14} + \frac{y ^{2}}{8} = 1

- 1.14 y^{2} = 52.3 + x^{2}

\frac{( x - 3 ) ^{2}}{\frac{2}{9}} + \frac{( y - 5 ) ^{2}}{25} = 1

What is 5x^2+3y^2-15=0 ?
The solution to 5x^2+3y^2-15=0 is Ellipse with (h,k)=(0,0),a=sqrt(3),b=sqrt(5)