Saved Bookmarks
| 1. |
find all the lines that pass through the point ` (1, 1)` and are tangent to the curve represent parametrically as `x = 2t-t^2` and `y = t + t^2`A. `(2sqrt(43))/(9)`B. 2C. 3D. `(2sqrt(53))/(9)` |
|
Answer» Correct Answer - D `x=2t-t^(2)" (i)"` and `y=t+t^(2)" (ii)"` `(dy)/(dx)=(dy//dt)/(dx//dt)=(1+2t)/(2-2t)` Slope of tangent using the point `(1,1)` and `(2t-t^(2),t+t^(2))" (iii)"` Equating (ii) and (iii), `(t+t^(2)-1)/(2t-t^(2)-1)=(1+2t)/(2-2t)` `rArr" "3t^(2)-4t+1=0` `rArr" "t=1,(1)/(3)` For `t=1`, point is `P(1,2)` and for `t=(1)/(3)`, point is Q`((5)/(9),(4)/(9))` `therefore" "PQ=(2sqrt(53))/(9)` |
|