0

Guest

Courses New

a=(a,0) and b=(-a,0) are two fixed points . P is a variable point such that PA and PB intercept a constant length k on a given line y=x find locus of point p

a=(a,0) and b=(-a,0) are two fixed points . P is a variable point such that PA and PB intercept a constant length k on a given line y=x find locus of point p

Grade:11

1 Answers

Vikas TU
14149 Points
5 years ago
Dear Student,
Let P=(r,s)
eqn of AP: y=s(x-a) /(r-a)
eqn of BP: y=s(x+a)/(r+a)
intersection of y=x and PA give point C by solving tre y=x and PA:
C=(as/(r-a-s),as/(r-a-s))
intersection of y=x and PB give point D by solving tre y=x and PB:
D=(as/(r+a-s),as/(r+a-s))
distance CD= sqrt(2(as/(r-a-s)-as/(r+a-s))^2)
=(sqrt(2)*a^2*s)/(r^2-2sr-a^2+s^2)
given this distance=k
=>k=(sqrt(2)*a^2*s)/(r^2-2sr-a^2+s^2)
=>kr^2+ks^2-sqrt(2)*a^2*s-2krs-ka^2=0
replacing r with x and s with y:
kx^2+ky^2-sqrt(2)*a^2*y-2kxy-ka^2=0 is the required locus of P. [ans]
 
Cheers!!
Regards,
Vikas (B. Tech. 4th year
Thapar University)

Think You Can Provide A Better Answer ?

Provide a better Answer & Earn Cool Goodies See our forum point policy

Other Related Questions on Analytical Geometry

View all Questions »

ASK QUESTION

Get your questions answered by the expert for free

Answer and earn gift vouchers

Win Gift vouchers upto Rs 500/-

View courses by askIITians

Design classes One-on-One in your own way with Top IITians/Medical Professionals

Click Here Know More

Complete Self Study Package designed by Industry Leading Experts

Click Here Know More

Live 1-1 coding classes to unleash the Creator in your Child

Click Here Know More

a Complete All-in-One Study package Fully Loaded inside a Tablet!

Click Here Know More