Note: Here, I am writing Alpha as a.
Given points are P(asina,acosa) and Q(acosa,-asina).
Distance between the two points PQ^2 = (x2 - x1)^2 + (y2 - y1)^2.
= > [(acosa - asina)]^2 + [(-asina - acosa)]^2
= > a^2cos^2a + a^2sin^2a - 2a^2cosasina + a^2sin^2a + a^2cos^2a + 2a^2sinacosa
= > a^2(cos^2a + sin^2a) + a^2(sin^2a + cos^2a)
= > a^2(1) + a^2(1)
= > 2a^2
Hope this helps!
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Answers & Comments
Verified answer
Note: Here, I am writing Alpha as a.
Given points are P(asina,acosa) and Q(acosa,-asina).
Distance between the two points PQ^2 = (x2 - x1)^2 + (y2 - y1)^2.
= > [(acosa - asina)]^2 + [(-asina - acosa)]^2
= > a^2cos^2a + a^2sin^2a - 2a^2cosasina + a^2sin^2a + a^2cos^2a + 2a^2sinacosa
= > a^2(cos^2a + sin^2a) + a^2(sin^2a + cos^2a)
= > a^2(1) + a^2(1)
= > 2a^2
Hope this helps!
Verified answer
We are asked to find the distance between the point P & Q,P = ( asinα , acosα )
Q = ( acosα , -asinα )
We know that,
Distance between the points ,
Now,
PQ = √[ ( asinα-acosα)² + (acosα + asinα)² ]
= √ [ a²(sin²α+cos²α) - 2a² sinαcosα + a² ( sin²α + cos²α ) + 2a²sinαcosα ]
= √ a² + a²
= √2 a
Formulae used :
1) sin²A + cos²A = 1
2) ( a + b )² = a² + b² + 2ab
Hope helped!