The line y = mx + c touches the parabola y^2 | vedclass

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

Question

(D) The equation of the parabola is $y^2 = 4a(x + a)$.Let $X = x + a$,then $x = X - a$. Substituting this into the equation,we get $y^2 = 4aX$.The con

Vedclass · Accepted Answer

$c = am + \frac{a}{m}$

Vedclass · Answer

(D) The equation of the parabola is $y^2 = 4a(x + a)$.Let $X = x + a$,then $x = X - a$. Substituting this into the equation,we get $y^2 = 4aX$.The condition for the line $y = mx + c$ to touch the parabola $y^2 = 4aX$ is $c' = \frac{a}{m}$,where $c'$ is the intercept on the $Y$-axis.Substituting $x = X - a$ into $y = mx + c$,we get $y = m(X - a) + c = mX + (c - am)$.Comparing this with $y = mX + c'$,we have $c' = c - am$.Equating the two expressions for $c'$,we get $c - am = \frac{a}{m}$.Therefore,$c = am + \frac{a}{m}$.

The line $y = mx + c$ touches the parabola $y^2 = 4a(x + a)$ if...

Similar Questions

If the line $2bx + 3cy + 4d = 0$ passes through the points of intersection of $y^2 = 4ax$ and $x^2 = 4ay$,then

The angle between the tangents drawn from the point $(1,4)$ to the parabola $y^2=4x$ is

If a normal chord of the parabola $y^2 = 4ax$ subtends a right angle at the vertex,its slope is-

$A$ circle has its center $C$ on the axis of a parabola and it touches the parabola at point $P$. The line segment $CP$ makes an angle of $120^{\circ}$ with the axis of the parabola. If the radius of the circle is $2$,then the latus rectum of the parabola is:

The equation of the common tangent touching the circle $(x - 3)^2 + y^2 = 9$ and the parabola $y^2 = 4x$ above the $x$-axis is

Vedclass Test Series

Exam Paper Generator

Online Exam Module