At its closest approach, a moon comes within 200,000 km of the planet it orbits. At that point, the moon is 300,000 km from the other focus of its orbit, f2. The planet is focus f1 of the moon's elliptical orbit. How far is the moon from the planet when it is 260,000 km from f2?

s₁ = 240,000 km

Explanation:

The distance between both the focuses f₁ and f₂ will be the sum of distances of the moon from each focus at a given point. Therefore,

s = s₁ + s₂

where,

s = total distance between the focuses = ?

s₁ = distance between f1 and moon = 200,000 km

s₂ = distance between f₂ and moon = 300,000 km

Therefore,

s = 200,000 km + 300,000 km

s = 500,000 km

Now, when the distance from f₂ becomes 260,000 km, then the distance from f₁(planet) will become:

s = s₁ + s₂

500,000 km = s₁ + 260,000 km

s₁ = 500,000 km - 260,000 km

s₁ = 240,000 km

ok

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