Question
The equation of a common tangent to the parabolas y=x^2 and y=-(x-2)^2 is
BITSAT
Mathematics
Parabola
2023
BITSAT 2023 (Memory Based Paper 1)
BITSAT Mathematics Question (2023) — Solution
Options
- A. y=4(x-2)
- B. y=4(x-1)
- C. y=4(x+1)
- D. y=4(x+2)
Answer
B. y=4(x-1)
Step-by-step solution
Equation of tangent of parabola y=x^2 be t x=y+a t^2 ...(i) y=t x- t^2 4 Solve with y =-( x -2)^2 t x- t^2 4 =-(x-2)^2 x^2+x(t-4)- t^2 4 +4=0 Here, Discriminant =0. (t-4)^2-4 (4- t^2 4 )=0 t^2-4 t=0 t=0 or t =4 Put value of t in eq. (i), then y=4(x-1).
Related: Mathematics — Parabola · All PYQ Banks