The equation of the latus rectum of a parabol | vedclass

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

Question

(D) The distance between the latus rectum and the tangent at the vertex of a parabola is equal to $a$, where $4a$ is the length of the latus rectum.Gi

Vedclass · Accepted Answer

$8 \sqrt{2} 	ext{ units}$

Vedclass · Answer

(D) The distance between the latus rectum and the tangent at the vertex of a parabola is equal to $a$, where $4a$ is the length of the latus rectum.Given the equations $x+y-8=0$ and $x+y-12=0$.The distance $a$ between these two parallel lines is given by the formula $d = \frac{|c_1 - c_2|}{\sqrt{A^2 + B^2}}$.$a = \frac{|-8 - (-12)|}{\sqrt{1^2 + 1^2}} = \frac{4}{\sqrt{2}} = 2 \sqrt{2}$.The length of the latus rectum is $4a$.Length $= 4 	imes (2 \sqrt{2}) = 8 \sqrt{2} 	ext{ units}$.

The equation of the latus rectum of a parabola is $x+y=8$ and the equation of the tangent at the vertex is $x+y=12$. Then the length of the latus rectum is

Similar Questions

$P$ and $Q$ are two points on the parabola $y^2 = 8x$ and $S$ is its focus. $PS$ and $QS$ meet the curve again in $T$ and $R$ respectively. If $PQ$ passes through a fixed point $(-2, 3)$,then $TR$ also passes through a fixed point whose coordinates are

The equation of the directrix of the parabola $y^2-x+4y+5=0$ is

What is the length of the latus rectum of the parabola $x = ay^2 + by + c$?

If $x-2y+k=0$ is a tangent to the parabola $y^2-4x-4y+8=0$,then the value of $k$ is

The length of the latus rectum of the parabola $9x^2 - 6x + 36y + 19 = 0$ is:

Vedclass Test Series

Exam Paper Generator

Online Exam Module