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What is the distance between the points P(m2,m2) and Q(m2,m2)

Question

What is the distance between the points
$P (m cos 2 α, m sin 2 α)$ and
$Q (m cos 2 β, m sin 2 β)?$

∣2 m sin (α - β) ∣

∣2 m cos (α - β) ∣

∣ m sin (2 α - 2 β) ∣

∣ m sin (2 α + 2 β) ∣

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Harper Discussed

What is the distance between the points

P (m cos 2 α, m sin 2 α)

and

Q (m cos 2 β, m sin 2 β)?

8 mins ago

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Text solutionVerified

distance formula is given by,

d = (x_{2} - x_{1})^{2} + (y_{2} - y_{1})^{2}

Given,

P = (m cos 2 α, m sin 2 α)

Q = (m cos 2 β, m sin 2 β)

= (m cos 2 β - m cos 2 α)^{2} + (m sin 2 β - m sin 2 α)^{2}

= m^{2} (- 2 cos 2 β cos 2 α - 2 sin 2 β sin 2 α + 2)

= m 2 (1 - (cos 2 β cos 2 α + sin 2 β sin 2 α))

= m 2 (1 - cos (2 α - 2 β))

= m 2 (2 sin^{2} (\frac{2 α - 2 β}{2}))

= 2 m sin (α - β)

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Question Text	What is the distance between the points $P (m cos 2 α, m sin 2 α)$ and $Q (m cos 2 β, m sin 2 β)?$
Answer Type	Text solution:1
Upvotes	150