Saved Bookmarks
| 1. |
Let A(x_(1),y_(1)) and B(x_(2),y_(2)) be two points on the parabola y^(2) = 4ax. If the circle with chord AB as a dimater touches the parabola, then |y_(1)-y_(2)| is equal to |
|
Answer» `4a` Solving it with `y^(2) =4ax`, we get `16a^(2) (y-y_(1)) (y-y_(2)) + (y^(2) -y_(1)^(2)) (y^(2)-y_(2)^(2)) =0` `rArr (y-y_(1)) (y-y_(2)) [16a^(2) + (y+y_(1)) (y+y_(2))] = 0` `rArr (y+y_(1)) (y+y_(2)) + 16a^(2) =0` `rArr y^(2) + (y_(1)+y_(2)) y + y_(1)y_(2) + 16a^(2) =0` The roots of the equation are equal if `(y_(1)+y_(2))^(2) = 4y_(1)y_(2) + 64A^(2) rArr |y_(1)-y_(2)| = 8a`. |
|