Question

The distance between the points (acosθ,0)(acos⁡θ,0)and (0,acosθ)(0,acos⁡θ)is…………………units.
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Answer 1

Answer:

$\sqrt{a^{2} +b^{2}$

Step-by-step explanation:

Given the point A(cosθ+bsinθ,0),(0,asinθ−bcosθ)

By distance formula,

The distance of AB=(x2​−x1​)2+(y2​−y1​)2

​=[0−(acosθ+bsinθ)2+(asinθ−bcosθ)−0]2

​=a2cos2θ+2abcosθsinθ+a2sin2θ+b2cos2θ−2absinθcosθ

​=(a2+b2)cos2θ+(a2+b2)sin2θ

​=a2+b2

​[∵cos2θ+sin2θ=1]