What is x^2+4y^2-25=0 ?

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

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x^2+4y^2-25=0

x^{2} + 4 y^{2} - 25 = 0

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

Solution steps

x^{2} + 4 y^{2} - 25 = 0

Rewrite

x^{2} + 4 y^{2} - 25 = 0

in the form of the standard ellipse equation

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

Therefore ellipse properties are:

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

a > b

therefore

a

is semi-major axis and

b

is semi-minor axis

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

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