Find the locus of the point of contact of the | vedclass

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

Question

(D) The equation of the parabola is $y^2 = 4x$. Comparing this with $y^2 = 4ax$,we get $a = 1$.The slope of the tangent $m = 	an(45^{\circ}) = 1$.The

Vedclass · Accepted Answer

None of these

Vedclass · Answer

(D) The equation of the parabola is $y^2 = 4x$. Comparing this with $y^2 = 4ax$,we get $a = 1$.The slope of the tangent $m = 	an(45^{\circ}) = 1$.The equation of a tangent to the parabola $y^2 = 4ax$ with slope $m$ is $y = mx + \frac{a}{m}$.Substituting $a = 1$ and $m = 1$,we get $y = 1(x) + \frac{1}{1}$,which simplifies to $y = x + 1$.The point of contact $(x_1, y_1)$ for a tangent with slope $m$ to the parabola $y^2 = 4ax$ is given by $(\frac{a}{m^2}, \frac{2a}{m})$.Substituting $a = 1$ and $m = 1$,we get the point of contact $(x_1, y_1) = (\frac{1}{1^2}, \frac{2(1)}{1}) = (1, 2)$.Since the point of contact is a fixed point $(1, 2)$,the locus is simply the point itself,which does not match any of the given algebraic expressions.

Find the locus of the point of contact of the tangent to the parabola $y^2 = 4x$,where the tangent makes an angle of $45^{\circ}$ with the $x$-axis.

Similar Questions

The latus rectum of the conic passing through the origin and having the property that the normal at each point $(x, y)$ intersects the $x$-axis at $(x + 1, 0)$ is:

Let $A$ and $B$ be two distinct points on the parabola $y^2 = 4x$. If the axis of the parabola touches a circle of radius $r$ having $AB$ as its diameter,then the slope of the line joining $A$ and $B$ can be

If the line $x + y = k$ is a normal to the parabola $y^2 = 4x$,find the value of $k$.

The distance of the point $(6, 4 \sqrt{3})$ from the focus of the parabola $y^2 = 8x$ is:

The equations of two sides of a variable triangle are $x = 0$ and $y = 3$,and its third side is a tangent to the parabola $y^2 = 6x$. The locus of its circumcentre is:

Vedclass Test Series

Exam Paper Generator

Online Exam Module