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

If $A(at^2, 2at)$,$B(a/t^2, -2a/t)$,and $C(a, 0)$,then $2a$ is equal to

The equation of a tangent to the parabola $y^2 = 4ax$ making an angle $\theta$ with the $x$-axis is

The ends of the latus rectum of the parabola $x^2 + 8y = 0$ are

If the focal distance of a point $P(2, y_1)$ on the parabola $y^2=kx$ is $3$,then the equation of the tangent drawn at $P$ to the given parabola is

The equation of the axis of the parabola $x^2 - 4x - 3y + 10 = 0$ is:

Vedclass Test Series

Exam Paper Generator

Online Exam Module