The vertex of a parabola is the point (a, b) | vedclass

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

Question

(B) The standard equation of a parabola with vertex at the origin $(0, 0)$ and axis along the positive $y$-axis is $X^2 = 4AY$,where the length of the

Vedclass · Accepted Answer

$(x - a)^2 = \frac{l}{2}(2y - 2b)$

Vedclass · Answer

(B) The standard equation of a parabola with vertex at the origin $(0, 0)$ and axis along the positive $y$-axis is $X^2 = 4AY$,where the length of the latus rectum $l = 4A$,so $A = \frac{l}{4}$.Substituting $A$,we get $X^2 = lY$.Given the vertex is at $(a, b)$,we use the transformation $X = x - a$ and $Y = y - b$.Substituting these into the equation,we get $(x - a)^2 = l(y - b)$.To match the given options,we can rewrite the right side as $(x - a)^2 = \frac{l}{2}(2y - 2b)$.

The vertex of a parabola is the point $(a, b)$ and the latus rectum is of length $l$. If the axis of the parabola is along the positive direction of the $y$-axis,then its equation is

Similar Questions

The angle between tangents to the parabola $y^2 = 4ax$ at the points where it intersects with the line $x - y - a = 0$ 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 $a$ and $c$ are the segments of a focal chord of a parabola and $b$ is the semi-latus rectum,then:

If the perpendicular distance from the focus of a parabola $y^2=4ax$ to its directrix is $\frac{3}{2}$,then the equation of the normal drawn at $(4a, -4a)$ is

The perpendicular distance from the origin to the focal chord drawn through the point $(4, 5)$ to the parabola $y^2 - 4y - 3x + 7 = 0$ is

Vedclass Test Series

Exam Paper Generator

Online Exam Module