Browse by Stream
QnA
Home
QnA
Go To Your Study Dashboard

Get Answers to all your Questions

header-bg qa
  • Home
  • Engineering
  • Locus of point of intersection of tangents at <img alt="\mathrm{(a \cos \alpha, b \sin \alpha) \text { and }(a \cos \beta, b \sin \beta)}" src="https://entrancecorner.onc

Locus of point of intersection of tangents at \mathrm{(a \cos \alpha, b \sin \alpha) \text { and }(a \cos \beta, b \sin \beta)}  for the ellipse \mathrm{\frac{x^2}{a^2}+\frac{y^2}{b^2}=1}  is, (given that (α – β) is a constant)

 

Option: 1

a circle


Option: 2

a straight line


Option: 3

an ellipse


Option: 4

a parabola

 


Answers (1)

best_answer

Point of intersection of tangents at \mathrm{(a \cos \alpha, b \sin \alpha) \text { and }(a \cos \beta, b \sin \beta)} is 

\mathrm{\left(a \frac{\cos \frac{\alpha+\beta}{2}}{\cos \frac{\alpha-\beta}{2}}, b \frac{\sin \frac{\alpha+\beta}{2}}{\cos \frac{\alpha-\beta}{2}}\right)}

\mathrm{\therefore \quad \text { required locus is } \frac{x^2}{a^2}+\frac{y^2}{b^2}=\sec ^2\left(\frac{\alpha-\beta}{2}\right)}

                                                             \mathrm{\text { [ } 8 \alpha-\beta \text { is given as constant }]}

which is the equation of an ellipse

 

Posted by

Pankaj Sanodiya

View full answer

JEE Main high-scoring chapters and topics

Study 40% syllabus and score up to 100% marks in JEE

Similar Questions

Latest Question