The equation of a tangent to the parabola y^2 | vedclass

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

Question

(D) The given tangent is $y = x + 2$,which is of the form $y = mx + c$ where $m = 1$ and $c = 2$.For a parabola $y^2 = 4ax$,the condition for $y = mx

Vedclass · Accepted Answer

$(-2, 0)$

Vedclass · Answer

(D) The given tangent is $y = x + 2$,which is of the form $y = mx + c$ where $m = 1$ and $c = 2$.For a parabola $y^2 = 4ax$,the condition for $y = mx + c$ to be a tangent is $c = a/m$.Here,$4a = 8$,so $a = 2$. Checking the condition: $c = 2/1 = 2$,which is satisfied.The locus of the intersection of two perpendicular tangents to a parabola is its directrix.The directrix of the parabola $y^2 = 8x$ is $x = -a$,which is $x = -2$.We are looking for a point on the line $y = x + 2$ that also lies on the directrix $x = -2$.Substituting $x = -2$ into the line equation: $y = -2 + 2 = 0$.Thus,the required point is $(-2, 0)$.

The equation of a tangent to the parabola $y^2 = 8x$ is $y = x + 2$. If another tangent is drawn to the parabola from a point on this line such that it is perpendicular to the given tangent,find the point.

Similar Questions

Let $P$ and $Q$ be points on the parabola $y^{2}=4x$ such that the line segment $PQ$ subtends a right angle at the vertex. If $PQ$ intersects the axis of the parabola at $R$, then the distance of the vertex from $R$ is

The equation of a curve in polar coordinates is $\frac{l}{r} = 2 \sin^2 \frac{\theta}{2}$. This equation represents:

If the tangents and normals at the extremities of a focal chord of a parabola $y^2 = 4ax$ intersect at $(x_1, y_1)$ and $(x_2, y_2)$ respectively,then:

Let $M$ be the foot of the perpendicular from a point $P$ on the parabola $y^2=8(x-3)$ onto its directrix and let $S$ be the focus of the parabola. If $\triangle SPM$ is an equilateral triangle,then $P$ is equal to

Let a line $y=mx$ $(m>0)$ intersect the parabola $y^{2}=x$ at a point $P$,other than the origin. Let the tangent to it at $P$ meet the $x$-axis at the point $Q$. If $\text{area}(\Delta OPQ)=4$ sq. units,then $m$ is equal to

Vedclass Test Series

Exam Paper Generator

Online Exam Module