Browse by Stream
QnA
Home
QnA
Go To Your Study Dashboard

Get Answers to all your Questions

header-bg qa
  • Home
  • Engineering
  • The angle between a pair of tangents drawn from a point P to the circle <img alt="\mathrm{x^2+y^2+4 x-6 y+9 \sin ^2 \alpha+13 \cos ^2 \alpha=0}" src="https://entrancecorner.oncodecogs.com/gif.

The angle between a pair of tangents drawn from a point P to the circle \mathrm{x^2+y^2+4 x-6 y+9 \sin ^2 \alpha+13 \cos ^2 \alpha=0}

is \mathrm{2a}. Then, the equation of the locus of P is \mathrm{x^2+y^2+4 x-6 y+k=0}, where k =

Option: 1

4


Option: 2

-9


Option: 3

-4


Option: 4

9


Answers (1)

best_answer

For the given circle, centre is (–2, 3), \mathrm{\text { radius }=2 \sin \alpha=A C}

In \mathrm{\triangle C A P}, let P be (h, k)

\mathrm{\begin{aligned} & \quad \sin \alpha=\frac{A C}{P C}=\frac{2 \sin \alpha}{C P} \\ & \Rightarrow \quad C P=2 \\ & \Rightarrow \quad 4=P C^2 \\ & \quad=(h+2)^2+(k-3)^2 \\ & \therefore \quad \text { Locus of } P(h, k) \text { is } \\ & \quad(x+2)^2+(y-3)^2=4 \\ & \text { Or } x^2+y^2+4 x-6 y+9=0 \\ & \Rightarrow \quad k=9 \end{aligned}}

 

Posted by

Ritika Harsh

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

NEET, JEE Main 2026: Wondering which college, course to pick? Careers360’s offline counselling from April 19
anam-khan

JEE Main 2026 final key soon; objection window closes today
anam-khan

100 marks in JEE Mains 2026 Percentile: Know rank trends, admission chances at NITs, IIITs

Latest Question