The length of the latus rectum of the parabol | vedclass

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

Question

(B) The focus of the parabola is $S = (1, -2)$.The equation of the directrix is $x + y + 3 = 0$.The distance from the focus to the directrix is denote

Vedclass · Accepted Answer

$2 \sqrt{2}$ units

Vedclass · Answer

(B) The focus of the parabola is $S = (1, -2)$.The equation of the directrix is $x + y + 3 = 0$.The distance from the focus to the directrix is denoted by $d$.The formula for the distance from a point $(x_1, y_1)$ to a line $ax + by + c = 0$ is $d = \frac{|ax_1 + by_1 + c|}{\sqrt{a^2 + b^2}}$.Substituting the values,$d = \frac{|1(1) + 1(-2) + 3|}{\sqrt{1^2 + 1^2}} = \frac{|1 - 2 + 3|}{\sqrt{2}} = \frac{2}{\sqrt{2}} = \sqrt{2}$.The length of the latus rectum of a parabola is $2 	imes (	ext{distance from focus to directrix})$.Length of latus rectum $= 2 	imes \sqrt{2} = 2 \sqrt{2}$ units.

The length of the latus rectum of the parabola whose focus is at $(1, -2)$ and directrix is the line $x + y + 3 = 0$ is

Similar Questions

If $x + y = k$ is a normal to the parabola ${y^2} = 12x$,then $k$ is

Two parabolas have the same focus $(4, 3)$ and their directrices are the $x$-axis and the $y$-axis,respectively. If these parabolas intersect at the points $A$ and $B$,then $(AB)^2$ is equal to

The equation of the tangent to the parabola $y^2 = 4x + 5$ parallel to the line $y = 2x + 7$ is

For a parabola with focus $(2, 1)$ and directrix $2x - 3y + 1 = 0$,what is the equation of the latus rectum?

The locus of the middle points of the chords of the parabola $y^2 = 4ax$ which pass through the origin is:

Vedclass Test Series

Exam Paper Generator

Online Exam Module