Home
Class 12
MATHS
The line joining the points (x ,2x)a n d...

The line joining the points `(x ,2x)a n d(3,5)` makes an obtuse angle with the positive direction of the x-axis. Then find the values of `xdot`

Text Solution

Verified by Experts

The correct Answer is:
`xin(5//2,3)`
The slope joining points `A(x,2x)` and `B(3,5)` is `(2x-5)//(x-3)` if AB makes an angle `theta` with the positive direction of the x-axis, then
`tan theta=(2x-5)/(x-3)`
Since, `theta` is obtuse, `tanthetalt0`
or `(2x-5)/(x-3)lt0`
or `x in ((5)/(2),3)`
Doubtnut Promotions Banner Mobile Dark
|

Topper's Solved these Questions

  • COORDINATE SYSYEM

    CENGAGE PUBLICATION|Exercise Concept applications 1.5|5 Videos

  • COORDINATE SYSYEM

    CENGAGE PUBLICATION|Exercise Concept applications 1.6|9 Videos

  • COORDINATE SYSYEM

    CENGAGE PUBLICATION|Exercise Concept applications 1.3|10 Videos

  • COORDINATE SYSTEM

    CENGAGE PUBLICATION|Exercise Multiple Correct Answers Type|2 Videos

  • CROSS PRODUCTS

    CENGAGE PUBLICATION|Exercise DPP 2.2|13 Videos

Similar Questions

Explore conceptually related problems

A straight line passes throught the point (-1,4) and makes an angle 60^(@) with the positive direction of the x- axis . Find the equation of the straight line.

Determine x so that the line passing through (3,4) and (x ,5) makes an angle of 135^0 with the positive direction of the x-axis.

Knowledge Check

  • The magnitude of the angle which the line y=-x makes with the positive direction of the x axis is -

    A
    `45^(@)`
    B
    `90^(@)`
    C
    `135^(@)`
    D
    `225^(@)`

    • Similar Questions

    Explore conceptually related problems

    A straight line passes through the point A(1,2) and makes an angle theta with the positive direction of x -axis . Find theta given that the distance of A from the point of intersection of this line with the line x+y=4 "is"(sqrt(6))/(3) unit.

    The line joining the points (-2,1,-8)a n d(a ,b ,c) is parallel to the line whose direction ratios are 6,2,a n d3. Find the values of a ,b and c

    A straight line passes throught the point P(3,-2) and makes an angle theta with the positive direction of x - axis Find theta , given that the distance of P from the point of intersection of this line with the line 3x+4y=4 is (3sqrt(2))/(5) units.

    If the equation of the pair of straight lines passing through the point (1,1) , one making an angle theta with the positive direction of the x-axis and the other making the same angle with the positive direction of the y-axis, is x^2-(a+2)x y+y^2+a(x+y-1)=0,a!=2, then the value of sin2theta is

    Write down a unit vector in XY-plane, making an angle of 30^(@) with the positive direction of x-axis.

    A circle of radius 5 units has diameter along the angle bisector of the lines x+y=2 and x-y=2. If the chord of contact from the origin makes an angle of 45^0 with the positive direction of the x-axis, find the equation of the circle.

    Find the angle which a line perpendicular to the line x-y+1=0 makes with the positive direction of the x axis.

    Home
    Profile