If the tangent to the curve x = at^2, y = 2at | vedclass

Name: Exam Paper Generator | JEE NEET Paper Generator | Vedclass
Brand: Vedclass
Rating: 5 (35 reviews)

Question

(A) Given the parametric equations of the curve: $x = at^2$ and $y = 2at$.First,find the derivatives with respect to $t$:$\frac{dx}{dt} = 2at$ and $\f

Vedclass · Accepted Answer

$(0, 0)$

Vedclass · Answer

(A) Given the parametric equations of the curve: $x = at^2$ and $y = 2at$.First,find the derivatives with respect to $t$:$\frac{dx}{dt} = 2at$ and $\frac{dy}{dt} = 2a$.The slope of the tangent is given by $\frac{dy}{dx} = \frac{dy/dt}{dx/dt} = \frac{2a}{2at} = \frac{1}{t}$.For the tangent to be perpendicular to the $x$-axis,the slope must be undefined (i.e.,$\frac{dy}{dx} 	o \infty$).This occurs when the denominator $t = 0$.Substituting $t = 0$ into the parametric equations:$x = a(0)^2 = 0$$y = 2a(0) = 0$Therefore,the point of contact is $(0, 0)$.

If the tangent to the curve $x = at^2, y = 2at$ is perpendicular to the $x$-axis,then what is the point of contact?

Similar Questions

The length of the chord of the parabola $x^2 = 4ay$ passing through its vertex and having slope $\tan\alpha$ is:

If the graph of $y = ax^2 - bx + c$ is as shown below,then the signs of $a$,$b$,and $c$ are:

Find the equation of the normal to the parabola $y^2 = 4x$ passing through the point $(3, 0)$.

The equation of the directrix of the parabola $y^2-x+4y+5=0$ is

The length intercepted by the curve $y^2 = 4x$ on the line satisfying $dy/dx = 1$ and passing through the point $(0, 1)$ is given by

Vedclass Test Series

Exam Paper Generator

Online Exam Module