MHT CET202012 Oct 2020Evening ShiftMathematicsStraight LinesActual
The locus of a point of intersection of two lines x 3 -y=k 3 and 3 k x+k y= 3 , k R , describes
Options
- Aa parabola
- Ba hyperbola
- Can ellipse
- Da pair of lines
Correct answer
B. a hyperbola
Step-by-step solution
We have aligned x 3 -y &=k 3 ...(1) 3 k x+k y &= 3 ...(2) aligned We will equate value of k from eq. (1) and (2) aligned & x 3 -y 3 = 3 3 x+y &(x 3 -y)(x 3 +y)=( 3 )( 3 ) & 3 x²-y²=3 3 x² 3 - y² 3 = 3 3 i.e. x² 1 - y² ( 3 )² =1, which is equation of hyperbola. aligned