Browse by Stream
QnA
Home
QnA
Go To Your Study Dashboard

Get Answers to all your Questions

header-bg qa
  • Home
  • Engineering
  • The locus of a point, which moves such that the sum of squares of its distances from the points (0,0),(3,0),(0,3),(3,3) is 64 units, is a circle of diameter d. Then <img alt="\mathrm{d^2}" src

The locus of a point, which moves such that the sum of squares of its distances from the points (0,0),(3,0),(0,3),(3,3) is 64 units, is a circle of diameter d. Then \mathrm{d^2} is equal to

Option: 1

46


Option: 2

48


Option: 3

50


Option: 4

44


Answers (1)

best_answer

Let P(x, y) be any point, according to the question, we have

\mathrm{\begin{gathered} (x-0)^2+(y-0)^2+(x-3)^2+(y-0)^2+(x-0)^2 \\ \quad+(y-3)^2+(x-3)^2+(y-3)^2=64 \\ \Rightarrow 4 x^2+4 y^2-12 x-12 y+36=64 \\ \Rightarrow \quad x^2+y^2-3 x-3 y=7 \end{gathered}}

\mathrm{\Rightarrow\left(x-\frac{3}{2}\right)^2+\left(y-\frac{3}{2}\right)^2=\frac{46}{4} \text {, which is equation of circle }}

\mathrm{\text { with radius, } r=\sqrt{\frac{46}{4}} \Rightarrow \text { Diameter, } d=2 \sqrt{\frac{46}{4}}}

\mathrm{\therefore \quad d^2=46}

Posted by

Gunjita

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

JAC Chandigarh Counselling 2025: Round 1 seat allotment result out for BTech admissions
anam-khan

JoSAA round 5 seat allotment result 2025 out on josaa.nic.in
anam-khan

BTech aspirant from north-east or UT? Apply for CSAB NEUT counselling 2025 today

Latest Question