Write the equation of ellipse if short axis is 2sqrt10. The point (10;-sqrt5) lies on the ellipse.

The equation of the ellipse
is:

x^2/a^2 + y^2/b^2 =
1

where a = long
semi-axis

           b = short
semi-axis

 To write the equation of the ellipse we'll have
to calculate a, because b, the short axis, is given by the
enunciation.

We also know that the ellipse passes through
the given point, meaning that the coordinates of the point are verifying the equation of
the ellipse.

x1^2/a^2 + y1^2/b^2 =
1

M(10,-sqrt5) belongs to ellipse if and only
if:

10^2/a^2 + (-sqrt5)^2/10 =
1

100/a^2 + 5/10 = 1

We'll add
-5/10 both sides:

100/a^2 = 1 -
5/10

100/a^2 = 5/10

We'll
divide by 5 both sides:

20/a^2 =
1/10

We'll cross multiply:

a^2
= 200

Now, we'll write the equation of the
ellipse:

x^2/a^2 + y^2/b^2 =
1

x^2/200 + y^2/10 =
1