The line x - b +lambda y = 0 cuts the pa...

The line `x - b +lambda y = 0` cuts the parabola `y^(2) = 4ax (a gt 0)` at `P(t_(1))` and `Q(t_(2))`. If `b in [2a, 4a]` then range of `t_(1)t_(2)` where `lambda in R` is

`[-4, -2]`

`(-4, -3]`

`[-3,-2]`

none of these

Text Solution

Verified by Experts

The correct Answer is:

Topper's Solved these Questions

MATHEMATICS
FIITJEE|Exercise OBJECTIVE|84 Videos
MATHEMATICS
FIITJEE|Exercise ASSERTION REASONING|8 Videos
MATHEMATICS
FIITJEE|Exercise NUMERICAL DECIMAL BASED QUESTIONS|15 Videos
MATHEMATICAL REASONING
FIITJEE|Exercise ASSIGNMENT PROBLEMS (OBJECTIVE) LEVEL-2|18 Videos
MATHEMATICS TIPS
FIITJEE|Exercise NUMERICAL DECIMAL BASED QUESTIONS|21 Videos

Similar Questions

Explore conceptually related problems

The line x - b + lamda. y = 0 cuts the parabola y^2 = 4ax (a>0) at P(t1) & Q(t2). If b in [2a, 4a] then range of t_1t_2 where lamda in R, is

If the normal to the parabola y^(2)=4ax at point t_(1) cuts the parabola again at point t_(2) then prove that t_(2)^(2)>=8

Normal at P(t1) cuts the parabola at Q(t2) then relation

If A (t_(1)) " and " B(t_(2)) are points on y^(2) = 4ax , then slope of AB is

If the normal to the parabola y^(2)=4ax at point t_(1) cuts the parabola again at point t_(2) .Then the minimum value of t_(2)^(2) is

The normal at t_(1) and t_(2) on the parabola y^(2)=4ax intersect on the curve then t_(1)t_(2)

Tangents drawn to the parabola y^(2)=8x at the points P(t_(1)) and Q(t_(2)) intersect at a point T and normals at P and Q intersect at a point R such that t_(1) and t_(2) are the roots of equation t^(2)+at+2=0;|a|>2sqrt(2) then locus of R is

The tangents to the parabola y^(2)=4ax at P(at_(1)^(2),2at_(1)), and Q(at_(2)^(2),2at_(2)), intersect at R Prove that the area of the triangle PQR is (1)/(2)a^(2)(t_(1)-t_(2))^(3)

If the tangents to the parabola y^(2)=4ax make complementary angles with the axis of the parabola then t_(1),t_(2)=

If A(at_(1)^(2),2at_(1)) and B(t_(2)^(2),2at_(2)) be the two points on the parabola y^(2)=4ax and AB cuts the x -axis at C sucrabola y^(2)=4ax and AC=3:1. show that t_(2)=-2t_(1) and if AB makes an angle of 90^(@) at the vertex,then find the coordinates of A and B.

FIITJEE-MATHEMATICS -ASSIGNMENT (SECTION(I) MCQ(SINGLE CORRECT)

If the focus of the parabola (y - k)^2 = 4(x - h) always lies between ...
Text Solution
|
A line drawn through the focus (F) and parallel to tangent at P(x, y) ...
Text Solution
|
The line x - b +lambda y = 0 cuts the parabola y^(2) = 4ax (a gt 0) at...
Text Solution
|
If the following informations is given about a parabola, then in which...
Text Solution
|
If the focus of a parabola is (2, 3) and its latus rectum is 8, then f...
Text Solution
|
Find the point on the axis of the parabola 3y^2+4y-6x+8 =0 from when ...
Text Solution
|
Find the point on the axis of the parabola 3y^2+4y-6x+8 =0 from when ...
Text Solution
|
If from a point on the line (x -1) =0, tangents are feawn to the parab...
Text Solution
|
The condition that a straight line with slope m will be normal to para...
Text Solution
|
The vertex V of the parabola y ^(2) = 4ax and two points on the parabo...
Text Solution
|
If P(theta),Q(theta+pi/2) are two points on the ellipse x^2/a^2+y^2/b^...
Text Solution
|
The area between the latusne latus rectum and tangents drawn at the en...
Text Solution
|
If SK be the perpendicular from the focus S on the tangent at any poin...
Text Solution
|
If the curves (x ^(2))/(4) + y ^(2) = 1 and (x ^(2))/(a ^(2)) + y ^(2)...
Text Solution
|
If eccentric angle of a point lying in the first quadrant on the ellip...
Text Solution
|
Prove that the common tangent of the ellipses (x^2)/(a^2)+(y^2)/(b^2)-...
Text Solution
|
If the ellipse (x^2)/(a^2-7)+(y^2)/(13=5a)=1 is inscribed in a square ...
Text Solution
|
The intercept made by the auxiliary circle of the ellipse (x ^(2))/(a ...
Text Solution
|
If the normal at P(2(3sqrt(3))/2) meets the major axis of ellipse (...
Text Solution
|
If y = 2x + c neither cuts the circle (x - 2)^2 + (y - 3)^2 = 4 nor th...
Text Solution
|