Question

find the equation such that the sum of the square of its distances from the two fixed points (a,0) and (-a,0) is constant

Answer 1

\[2x^{2}/a+y^{2}/b =C\]

Answer 2

its an elipse

Answer 3

the definition itself of this curve is that the distance of every point on it is the sum of the distances from two point called foci

Answer 4

Then just folow what the problem says:
\[\sqrt{(x-a)^{2}+y ^{2}} + \sqrt{(x+a)^{2}+y ^{2}} = C\]
and just rearange this a bit.

Answer 5

this is how more or less this could look.
the slope is the tangent of the angle. so \[\alpha = arctg (-2/3)\]
but you need angle with y axis, so it would be 90 - alpha

Answer 6

sry, mistake, :)

but you need angle with y axis, so it would be 180 - alpha