Home
Class 12
MATHS
Find the distance between the points P(a...

Find the distance between the points `P(asinalpha, acosalpha)` and `Q(a cos alpha,-a sinalpha)`

Text Solution

Verified by Experts

The correct Answer is:
NA
`PQ=sqrt(a^2(cosalpha-cosbeta)^2=a^2(sinalpha-beta)^2)`
`a=sqrt(sin^2alpha+cos^2alpha+cos^2beta+sin^2beta-2cosalphacosbeta-2sinalphasinbeta)`
`a=sqrt(2(1-cos(alpha-beta))`
`a=sqrt(2xx2sin^(2).(alpha-beta)/(2))`
`=2a"sin"(alpha-beta)/(2)`
Promotional Banner

Topper's Solved these Questions

  • COORDINATE SYSYEM

    CENGAGE PUBLICATION|Exercise Concept applications 1.3|10 Videos

  • COORDINATE SYSYEM

    CENGAGE PUBLICATION|Exercise Concept applications 1.4|8 Videos

  • COORDINATE SYSYEM

    CENGAGE PUBLICATION|Exercise Concept applications 1.1|6 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

The distance between the point ( acosalpha,asinalpha) and ( acosbeta,asinbeta) is

Find the distance between the pair of points (a, b) and (-a, -b)

Find the distance bwtween the points P(1,-3,4) and Q(-4,1,2)

Find the values of y for which the distance between the points P(2, -3) and Q(10, y) is 10 units.

If a straight line through the origin bisects the line passing through the given points (acosalpha,asinalpha) and (acosbeta,asinbeta), then the lines

Show that the image of the point (h,k) with respect to the striaight line x cos alpha+ y sin alpha=p is the point (2 p cos alpha- h cos2 alpha- k sin 2 alpha, 2p sin alpha- h sin 2 alpha- k cos 2 alpha) .

Prove that the product of the matrices {:[(cos ^(2)alpha,cos alpha sin alpha ),(cos alpha sinalpha, sin^(2)alpha)]and {:[(cos ^(2)beta,cosbetasinbeta),(cos betasinbeta,sin^(2)beta)] is the null matrix when alpha and beta differ by an odd multiple of (pi)/(2) .

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, " then prove that 4p^(2) + q^(2) = a^(2).

Find the value of sin^6 alpha+ cos^6 alpha+ 2sin^2 alpha cos^2 alpha .

If tantheta=(sin alpha-cos alpha)/(sinalpha+cosalpha)1 then