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If the tangent at a point `P` with parameter `t`, on the curve `x=4t^2+3`, `y=8t^3-1` `t in R` meets the curve again at a point Q, then the coordinates of Q are |
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Answer» `x=4t^2+3` dif. with respect to t `y=8t^2-1` difff. wih respect to t `dy/dx=(dy/dt)*(dx/dt)=(24t^2)/(8t)=3t` `(y-y_1)=(8t)*(x-x_1)` `9-(8t_1^3-1)-3t_1{n-t_1^2-3}` `8t^3-1-8t_1^3+1=3t_1{4t^2+3-4t_1^2-3}` `8(t-t_1){t^2+t_1^2+tt_1}-12t_1{t-t-1}(t_1+t)` `8t^2-4t_1^2-4t_t_1=0` `2t^2-t_1^2-tt_1=0` `(t^2-t_1)+t^2-tt_1=0` `(t-t_1)(t+t_1)+t(t-t_1)=0` `t+t_1+t=0` `t=-t_1/2` `x=4*(t_1/2)^2+3=3+t_1^2` `y=8*(-t_1/2)^3-1` `=t_1^3-1` option d is correct. |
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