Q. 145.0( 7 Votes )

If the coordinates of P and Q are (a cos θ, b sin θ) and (–a sin θ, b cos θ) respectively, then prove that OP2 + OQ2 = a2 + b2, where O is the origin.

Answer :

We have P (a cos θ, b sin θ)


Q (–a sin θ, b cos θ)


We know that distance of a point A (x,y) from origin O (0, 0) is given as OA =


Using the above formula,


OP =


=


OP2 =


OQ =


=


OQ2 =


Now, OP2 + OQ2 = a2 cos2θ + b2 sin2θ + a2 sin2θ + b2 cos2θ


= a2 (cos2θ +sin2θ) + b2 (sin2θ + cos2θ)


We know that, cos2θ +sin2θ =1


OP2 + OQ2 = a2 + b2


Rate this question :

How useful is this solution?
We strive to provide quality solutions. Please rate us to serve you better.
Related Videos
Chemical Co-ordination VS Neural Co-ordinationChemical Co-ordination VS Neural Co-ordinationChemical Co-ordination VS Neural Co-ordination48 mins
Quiz | Chemical Co-ordinationQuiz | Chemical Co-ordinationQuiz | Chemical Co-ordination47 mins
Some Interesting Proofs in GeometrySome Interesting Proofs in GeometrySome Interesting Proofs in Geometry36 mins
Section FormulaSection FormulaSection Formula30 mins
Quiz | Neural  Co-ordinataionQuiz | Neural  Co-ordinataionQuiz | Neural Co-ordinataion51 mins
Previous Year RMO QuestionsPrevious Year RMO QuestionsPrevious Year RMO Questions43 mins
NCERT | Most Important Proofs for BoardsNCERT | Most Important Proofs for BoardsNCERT | Most Important Proofs for Boards28 mins
Foundation | Human Endocrine SystemFoundation | Human Endocrine SystemFoundation | Human Endocrine System58 mins
Human BrainHuman BrainHuman Brain52 mins
Tropic and Nastic MovementsTropic and Nastic MovementsTropic and Nastic Movements32 mins
Try our Mini CourseMaster Important Topics in 7 DaysLearn from IITians, NITians, Doctors & Academic Experts
Dedicated counsellor for each student
24X7 Doubt Resolution
Daily Report Card
Detailed Performance Evaluation
caricature
view all courses