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Question
Find the distance between the points
P(a sin ∝,a cos ∝ )and Q( acos ∝ ,- asin ∝)
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Solution
P( a sin ∝,a cos ∝ ) and Q(a cos a ,- a sin ∝)
The given points are P( a sin ∝,a cos ∝ ) and Q(a cos a ,- a sin ∝)
`Then (x_1 = a sin , y_1 = a cos ∝ ) and (x_2 = a cos a , y_2 = - a sin ∝ )`
`PQ = sqrt( (x_2 -x_1)^2 + (y_2-y_1)^2)`
`= sqrt(( a cos ∝ - a sin ∝ )^2 + ( -a sin ∝ - a cos ∝ )^2)`
`=sqrt((a^2 cos^2 ∝ + a^2 sin^2 ∝ - 2a^2 cos ∝ xx sin ∝ )+(a^2 sin^2 ∝ + a^2 cos^2 ∝ +2a^2 cos ∝ xx sin ∝ ))`
`= sqrt(2a^2 cos^2 ∝ +2a^2 sin^2 ∝ )`
`= sqrt(2a^2 (cos^2 ∝ + sin^2 ∝ ))`
`= sqrt( 2a^2 (1)) ("From the identity" cos^2 ∝ + sin^2 ∝=1 )`
`=sqrt(2a^2)`
`= sqrt(2a)` units
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