The line lx + my + n = 0 will touch the parab | vedclass

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

Question

(C) The given line is $lx + my + n = 0$,which can be rewritten as $y = -\frac{l}{m}x - \frac{n}{m}$.The condition for a line $y = mx + c$ to be tangen

Vedclass · Accepted Answer

$ln = am^2$

Vedclass · Answer

(C) The given line is $lx + my + n = 0$,which can be rewritten as $y = -\frac{l}{m}x - \frac{n}{m}$.The condition for a line $y = mx + c$ to be tangent to the parabola $y^2 = 4ax$ is $c = \frac{a}{m}$.Here,the slope of the line is $M = -\frac{l}{m}$ and the intercept is $C = -\frac{n}{m}$.Substituting these into the condition $C = \frac{a}{M}$,we get:$-\frac{n}{m} = \frac{a}{-l/m}$$-\frac{n}{m} = -\frac{am}{l}$$ln = am^2$.

The line $lx + my + n = 0$ will touch the parabola $y^2 = 4ax$,if

Similar Questions

The shortest distance between the line $y = x$ and the curve $y^2 = x - 2$ is

If the line $x = my + k$ touches the parabola $x^2 = 4ay$,then $k = $

Two parabolas have the same focus. If their directrices are the $x$-axis and the $y$-axis respectively,then the slope of their common chord is:

If the line $x + y - 1 = 0$ is tangent to the parabola $y^2 = kx$,find the value of $k$.

From a point $(d, 0)$, three normals are drawn to the parabola $y^{2} = x$. Then:

Vedclass Test Series

Exam Paper Generator

Online Exam Module