If the vertex of a parabola is (2, 0) and the | vedclass

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

Question

(D) The axis of the parabola is the line passing through the vertex and perpendicular to the directrix. Since the directrix is the $y$-axis $(x = 0)$,

Vedclass · Accepted Answer

$(4, 0)$

Vedclass · Answer

(D) The axis of the parabola is the line passing through the vertex and perpendicular to the directrix. Since the directrix is the $y$-axis $(x = 0)$,the axis of the parabola is the $x$-axis.Let the focus be $S(a, 0)$.The vertex is the midpoint of the segment joining the focus and the point of intersection of the axis and the directrix.The point of intersection of the axis ($x$-axis) and the directrix ($y$-axis) is $Z(0, 0)$.Since the vertex $(2, 0)$ is the midpoint of $ZS$,we have:$\frac{a + 0}{2} = 2 \implies a = 4$.Thus,the focus is $(4, 0)$.

If the vertex of a parabola is $(2, 0)$ and the $y$-axis is its directrix,find its focus.

Similar Questions

The line $y = 6x + 1$ touches the parabola $y^2 = 24x$. The coordinates of a point $P$ on this line,from which the tangent to $y^2 = 24x$ is perpendicular to the line $y = 6x + 1$,is

If the focal chord drawn through the point $P(5,5)$ to the parabola $y^2=5x$ meets the parabola again at the point $Q$,then the tangent drawn to this parabola at $Q$ meets the axis of the parabola at the point

The largest value of $k$ for which the circle $x^2+y^2=k^2$ lies completely in the interior of the parabola $y^2=4x+16$ is

The tangents to the parabola $y^2 = 4ax$ from an external point $P$ make angles $\theta_1$ and $\theta_2$ with the axis of the parabola,such that $\tan \theta_1 + \tan \theta_2 = b$,where $b$ is a constant. Then $P$ lies on

If the parabolas $y^2 = 4b(x - c)$ and $y^2 = 8ax$ have a common normal,then which one of the following is a valid choice for the ordered triad $(a, b, c)$?

Vedclass Test Series

Exam Paper Generator

Online Exam Module