If one end of a focal chord of the parabola y | vedclass

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

Question

(A) The equation of the parabola is $y^2 = 16x$. Comparing this with $y^2 = 4ax$,we get $4a = 16$,so $a = 4$.The focus of the parabola is $S(a, 0) = (

Vedclass · Accepted Answer

$25$

Vedclass · Answer

(A) The equation of the parabola is $y^2 = 16x$. Comparing this with $y^2 = 4ax$,we get $4a = 16$,so $a = 4$.The focus of the parabola is $S(a, 0) = (4, 0)$.Let the coordinates of one end of the focal chord be $A(at_1^2, 2at_1) = (1, 4)$.Since $a = 4$,we have $4t_1^2 = 1$ $\Rightarrow t_1^2 = \frac{1}{4}$ $\Rightarrow t_1 = \frac{1}{2}$ (since $y > 0$).For a focal chord,the product of the parameters of the endpoints is $t_1 t_2 = -1$. Thus,$t_2 = -\frac{1}{t_1} = -2$.The length of a focal chord with parameter $t$ is given by $L = a(t + \frac{1}{t})^2$.Substituting $t = t_1 = \frac{1}{2}$,we get:$L = 4(\frac{1}{2} + \frac{1}{1/2})^2 = 4(\frac{1}{2} + 2)^2 = 4(\frac{5}{2})^2 = 4 	imes \frac{25}{4} = 25$.

If one end of a focal chord of the parabola $y^2 = 16x$ is at $(1, 4)$,then the length of this focal chord is

Similar Questions

Let the line $y - \sqrt{3}x + 3 = 0$ cut the parabola $2y^2 = 2x + 3$ at $A$ and $B$. If $P(\sqrt{3}, 0)$,then the value of $|PA - PB|$ is [where $PA$ denotes the distance between points $P$ and $A$].

The equation of the tangent to the parabola $y^2=16x$,which is perpendicular to the line $3x-4y+5=0$,is given by

If $m_1$ and $m_2$ are the slopes of the tangents drawn from the point $(1, 4)$ to the parabola $y^2 = 11x$,then $2(m_1^2 + m_2^2) = $

If the vertex of the conic $y^{2}-4y=4x-4a$ always lies between the straight lines $x+y=3$ and $2x+2y-1=0$, then:

Three normals drawn from any point to the parabola $y^2 = 4ax$ cut the line $x = 2a$ in points whose ordinates are in arithmetical progression. Then the tangents of the angles which the normals make with the axis of the parabola are in:

Vedclass Test Series

Exam Paper Generator

Online Exam Module