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Find the Distance Between the Points P(A Sin ∝,A Cos ∝ )And Q( Acos ∝ ,- Asin ∝) - Mathematics

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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 

Concept: Distance Formula
  Is there an error in this question or solution?

APPEARS IN

RS Aggarwal Secondary School Class 10 Maths
Chapter 16 Coordinate Geomentry
Q 1.6

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