Question

If the tangent at a point P, with parameter t, on the curve $x=4t^2+3,y=8t^3-1,tϵR$ meets the curve again at a point Q, then the coordinates of Q are:

• A. $(t^2+3,-t^3-1)$
• B. $(4t^2+3,-8t^3-1)$
• C. $(16t^3+3,-64t^3-1)$
• D. $(t^2+3,t^3-1)$

Answer 1

The correct option is A $(t^2+3,-t^3-1)$

$\frac{dx}{dt}=8t$ and $\frac{dy}{dt}=24t^2$
$\frac{dy}{dx}=3t$
$y-y_1=m(x-x_1)$
$y-(8t^3-1)=3t(x-4t^2-3)$
Equation is $y=3tx-4t^3-9t-1$
We can subsitute and check that option $A$ satisfies the equation.