InterviewSolution
Saved Bookmarks
InterviewSolution
| 1. |
If from any point `P` on the circle `x^2+y^2+2gx+2fy+c=0`, tangents are drawn to the circle `x^2+y^2+2gx+2fy+csin^2 alpha+(g^2+f^2)cos^2 alpha=0`, then the angle between the tangents is :(A) `alpha`(B) `2 alpha`(C) `alpha/2`(D) `alpha/3` |
|
Answer» P(h,k) to the cords `x^2+y^2+2xy+2fy=0` `T=h^2+k^2+2gh+2fk+c` `T=h^2+k^2+2gh+2fk+sin^alpha+(g^2+f^2)cos^2alpha` `sintheta(h,k)` lies on the circle `x^2+y^2+2gx+2fy+c=0` `t^2=(h^2+k^2gh+2fk+c)+csin^alpha+(g^2+f^2)cos^2alpha-c` `=(g^2+f^2)cos^2alpha-c(1-sin^2alpha)` `r^2=g^2f^2-(csin^2alpha+(g^2+f^2)cos^2alpha)` `=(g^2+f^2-c)sin^2alpha` `tantheta=r/T=sqrt((g^2+f^2-c)sin^2alpha)/sqrt(g^2+f^2-c cos^2alpha)` `sqrt(sin^2alpha/cos^2alpha)=tanalpha` `theta=alpha` option b is coorect |
|