Question
The locus of the point of intersection of the lines x=a ( 1-t^2 1+t^2 ) and y= 2 a t 1+t^2 represent (t being a parameter)
BITSAT
Mathematics
Straight Lines
2024
BITSAT 2024 (Memory Based Paper 3)
BITSAT Mathematics Question (2024) — Solution
Options
- A. Circle
- B. Parabola
- C. Ellipse
- D. Hyperbola
Answer
A. Circle
Step-by-step solution
Given x=a ( 1-t^2 1+t^2 ) and y= 2 a t 1+t^2 aligned & Let t= \\ & x=a ( 1- ^2 1+ ^2 ) \\ & and y= 2 a 1+ ^2 \\ & x=a 2 and y=a 2 \\ & 2 = x a and 2 = y a aligned Squaring both sides, we get ^2 2 = x^2 a^2 ....(i) and ^2 2 = y^2 a^2 ....(ii) Adding Eqs. (i) and (ii), we get aligned ^2 2 + ^2 2 & = x^2 a^2 + y^2 a^2 \\ x^2+y^2 & =a^2 aligned Locus is a circle having centre at origin and radius a.
Related: Mathematics — Straight Lines · All PYQ Banks