10th Class Mathematics Coordinate Geometry Question Bank MCQs - Coordinate Geometry

The distance between the points \[P(a\,\sin \phi ,\,0)\] and \[Q(0,-a\,\cos \phi )\] is:

A) \[{{a}^{2}}\]

B) \[1\]

C) \[2a\]

D) \[a\]

Correct Answer: D

Solution :

[d] \[PQ=\sqrt{{{(0-a\sin \phi )}^{2}}+{{(-a\cos \phi -0)}^{2}}}\]

\[=\sqrt{{{a}^{2}}{{\sin }^{2}}\phi +{{a}^{2}}{{\cos }^{2}}\phi }=a\sqrt{{{\sin }^{2}}\phi +{{\cos }^{2}}\phi }=a\sqrt{1}=a\]