Home
Class 11
MATHS
If p and q are the lengths of the perpen...

If `p` and `q` are the lengths of the perpendiculars from the origin to the straight lines `x sec alpha+y cosec alpha=a` and `x cos alpha-y sin alpha=a cos 2alpha, ` prove that `4p^(2)+q^(2)=a^(2)`

Answer

Step by step text solution for If p and q are the lengths of the perpendiculars from the origin to the straight lines x sec alpha+y cosec alpha=a and x cos alpha-y sin alpha=a cos 2alpha, prove that 4p^(2)+q^(2)=a^(2) by MATHS experts to help you in doubts & scoring excellent marks in Class 11 exams.

Doubtnut Promotions Banner Mobile Dark
|

Topper's Solved these Questions

  • STRAIGHT LINES

    AAKASH SERIES|Exercise EXERCISE 3.5 (VERY SHORT ANSWER QUESTIONS)|9 Videos

  • STRAIGHT LINES

    AAKASH SERIES|Exercise EXERCISE 3.5 ( SHORT ANSWER QUESTIONS)|14 Videos

  • STRAIGHT LINES

    AAKASH SERIES|Exercise EXERCISE 3.4( SHORT ANSWER QUESTIONS)|17 Videos

  • REVISION EXERCISE

    AAKASH SERIES|Exercise PROPERTIES OF TRIANGLES|57 Videos

  • TANGENT AND NORMAL

    AAKASH SERIES|Exercise ADVANCED SUBJECTIVE TYPE QUESTIONS|48 Videos

Similar Questions

Explore conceptually related problems

If p and q are the lengths of the perpendiculars from the origin to the straight lines x sec alpha+ycosec alpha=a and x cos alpha-y sin alpha = a cos 2alpha , prove that 4p^(2)+q^(2)=a^(2) .

sin^(2) alpha * tan alpha + cos^(2) alpha * cot alpha + 2 sin alpha cos alpha =

Knowledge Check

  • The perpendicular distance from origin to the line x/(p sec alpha)+y/(p cosec alpha)=1 is

    A
    `| p sin 2alpha|`
    B
    `|p cos 2 alpha|`
    C
    `|p tan 2alpha|`
    D
    `|p|`

  • If p and q are the perpendicular distances from the origin to the straight lines x sec theta - y cosec theta = a and x cos theta + y sin theta = a cos 2 theta , then

    A
    `4p^2 + q^2 = a^2`
    B
    `p^2 + q^2 = a^2`
    C
    `p^2 + 2q^2 = a^2`
    D
    `4p^2 + q^2 = 2a^2`

  • The foot of the perpendicular from (0, 0) to the line x cos alpha+y sin alpha=p is

    A
    `(cos alpha, sin alpha)`
    B
    `(p cos alpha, p sin alpha)`
    C
    `(p//cos alpha, p//sin alpha)`
    D
    `(p sin alpha, p cos alpha)`

    • Similar Questions

    Explore conceptually related problems

    The locus of the point of intersection of the lines x cos alpha + y sin alpha=a and x sin alpha-y cos alpha=b , where alpha is a parameter is

    The locus of the point of intersection of the lines x cos alpha+y sin alpha =a and x sin alpha-y cos alpha=b , where alpha is a parameter is

    If x=a ( " cosec " alpha + cot alpha) and y=(b(1- cos alpha))/(sin alpha ) , then

    If (sin alpha )/(a) = ( cos alpha )/(b) , then a sin 2alpha + b cos 2 alpha =

    The angle between the lines x cos alpha + y sin alpha=p_(1) and x cos beta+y sin beta=p_(2) where alpha gt beta is

    Home
    Profile