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If x = h + a cos θ and y = k + a sin θ, prove that (x – h)2 + (y – k)2 = a2.

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This is an important question from the
Book- ML Aggarwal
Board- ICSE
Publication- Avichal
Chapter- Trigonometric Identities
Chapter number-18
If x = h + a cos θ and y = k + a sin θ, prove that (x – h)2 + (y – k)2 = a2.

Trigonometric Identities, class 10th, chapter 18th, question no 35,  ICSE board, ML aggarwal..

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1 Answer

  1. We have been Given,

    x = h + a cos θ

    y = k + a sin θ

    Now,

    x – h = a cos θ

    y – k = a sin θ

    On squaring and adding we get

    (x – h)2 + (y – k)2 = a2 cos2 θ + a2 sin2 θ

    = a(sin2 θ + cos2 θ)

    = a2 (1) [Since, sin2 θ + cos2 θ = 1]

    – Hence proved

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