Browse by Stream
QnA
Home
QnA
Go To Your Study Dashboard

Get Answers to all your Questions

header-bg qa
  • Home
  • Engineering
  • If is the perpendicular from a point on a rectangular hyperbola to its a

If \mathrm{PN} is the perpendicular from a point on a rectangular hyperbola to its asymptotes, the locus, the mid-point of \mathrm{PN} is 
 

Option: 1

Circle


Option: 2

Parabola


Option: 3

Ellipse


Option: 4

Hyperbola


Answers (1)

best_answer

Let \mathrm{xy=c^{2}} be the rectangular hyperbola, and let \mathrm{P(x_{1},y_{1})} be a point on it. Let \mathrm{Q(h,k)} be the mid-point of \mathrm{PN}. Then the coordinates of \mathrm{Q} are \mathrm{\left(x_1, \frac{y_1}{2}\right)}
\mathrm{\therefore x_1=h \text { and } \frac{y_1}{2}=k \Rightarrow x_1=h \text { and } y_1=2 k}
But \mathrm{(x_{1},y_{1})} lies on \mathrm{xy=c^{2}}
\mathrm{\therefore \quad h \cdot(2 k)=c^2 \Rightarrow h k \Rightarrow c^2 / 2}
Hence, the locus of \mathrm{(h,k)} is \mathrm{x y=c^2 / 2}, which is a hyperbola.

Posted by

Kuldeep Maurya

View full answer

JEE Main high-scoring chapters and topics

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

Similar Questions

Trending Articles/News

anam-khan

JEE Main 2025: 2nd attempt? Mistakes to avoid, tips to improve score, percentile
anam-khan

JEE Main 2025: What to expect on exam day? Section-wise paper pattern, marking scheme, last-minute tips
anam-khan

JEE Main 2025 Live: NTA JEE session 2 exams from tomorrow; updates on admit card, exam pattern, passing marks

Latest Question