1.

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

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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