Find the distance between the points:
P(a sin a, acos a) and Q(a cos a, – a sin a)
In this question, we have to use the distance formula to find the distance between two points which is given by, say for points P(x1,x2) and Q(y1,y2) then
PQ = √(x2 – x1)2 + (y2 – y1)2
PQ = √{(a cos a – a sin a)2 – (– a sin a – a cos a)2}
= √{(a2 cos2 a + a2 sin2 a – 2a2 sina.cosa + a2 cos2 a + a2 sin2 a + 2a2 sina.cosa }
= √{ a2 (cos2 a + sin2 a) + (a2 (cos2 a + sin2 a))}
= √a2(1) + a2 (1)
= √a2(1 + 1)
∴ PQ = a√2 units
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