InterviewSolution
Saved Bookmarks
| 1. |
A tangent is drawn at any point P(t) on the parabola y^(2)=8x and on it is takes a point Q(alpha,beta) from which a pair of tangent QA and OB are drawn to the circle x^(2)+y^(2)=8. Using this information, answer the following questions : The locus of the point of concurrecy of the chord of contact AB of the circle x^(2)+y^(2)=4 is |
|
Answer» `y^(2)-2x=0` (3) The equation of the tangent at point P of the PARABOLA `y^(2)=8x` is `yt=x+2T^(2)`(1) The equation of the chord of contact of the circle `x^(2)+y^(2)=8` w.r.t. `Q(alpha,beta)` is `xalpha+ybeta=8`(2) `Q(alpha.beta)` lies on (1). Hence, `betat=alpha+2t^(2)`(3) `:.xalpha+y((alpha)/(t)+2t)-8=0`[From (2) and (3)] `OR2(ty-4)+alpha(x+(y)/(t))=0` For point of concurrency, `x=-(y)/(t)andy=(4)/(t)` Therefore, the LOCUS is `y^(2)+4x=0` |
|