What is the length of the latus rectum of the | vedclass

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

Question

(B) The given equation is $x = ay^2 + by + c$.We can rewrite this by completing the square for $y$:$x = a(y^2 + \frac{b}{a}y) + c$$x = a(y^2 + \frac{b

Vedclass · Accepted Answer

$\frac{1}{|a|}$

Vedclass · Answer

(B) The given equation is $x = ay^2 + by + c$.We can rewrite this by completing the square for $y$:$x = a(y^2 + \frac{b}{a}y) + c$$x = a(y^2 + \frac{b}{a}y + \frac{b^2}{4a^2}) + c - \frac{b^2}{4a}$$x - (c - \frac{b^2}{4a}) = a(y + \frac{b}{2a})^2$$(y + \frac{b}{2a})^2 = \frac{1}{a}(x - (c - \frac{b^2}{4a}))$This is in the standard form $(y - k)^2 = 4p(x - h)$,where $4p = \frac{1}{a}$.The length of the latus rectum is given by $|4p|$.Therefore,the length is $|\frac{1}{a}| = \frac{1}{|a|}$.

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

Similar Questions

The coordinates of the extremities of the latus rectum of the parabola $5y^2 = 4x$ are

Find the length of the subnormal of the parabola $y^2 = 16x$ at the point where the $x$-coordinate is $4$.

The parabola with directrix $x+2y-1=0$ and focus $(1,0)$ is

The length of the latus rectum of the parabola $169\{(x-1)^2+(y-3)^2\}=(5x-12y+17)^2$ is

Which of the following represents a parabola?

Vedclass Test Series

Exam Paper Generator

Online Exam Module