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Find the slope of the line joining the p...

Find the slope of the line joining the points `(a cos theta , b sin theta)` and `(a cos phi, b sin phi)`

Text Solution

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`(b(sin theta - sin phi))/(a (cos theta - cos phi))`
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Find perpendicular distance from the origin of the line joining the points (cos theta, sin theta) and (cos phi, sin phi)

If the line joining the points (a cos theta , b sin theta) and (a cos phi, b sin phi) .Prove that the equation of this lines is x/a "cos" (theta + phi)/2 + y/b"sin" (theta + phi)/2 = "cos" (theta -phi)/2

Knowledge Check

  • The product of matrices A = [(cos^(2) theta, cos theta sin theta),(cos theta sin theta , sin^(2) theta)] and sin B = [(cos^(2)phi, cos phi sin phi),(cos phi sin phi, sin^(2) phi)] is a null matrix if theta - phi =

    A
    `2 n pi, n in Z`
    B
    `n (pi)/(2), n in Z`
    C
    `(2n+ 1) (pi)/(2) , n in Z`
    D
    `n pi, n in Z`

  • The equation of a straight line which passes through the point (a cos^(3) theta, a sin^(3) theta) and perpendicular to x sec theta + y " cosec " theta = a is

    A
    `(x)/(a) + (y)/(a) = a cos theta`
    B
    `x cos theta - y sin theta = a cos 2 theta`
    C
    `x cos theta + y sin theta= a cos theta`
    D
    `x cos theta + y sin theta - a cos 2 theta = 1`

  • If beta is one of the angles between the normals to the ellipse, x^(2) + 3y^(2) = 9 at the points (3cos theta, sqrt(3) sin theta) and (-3sin theta, sqrt(3) cos theta), theta in (0, (pi)/(2))," then "(2 cot beta)/(sin 2 theta) is equal to

    A
    `(2)/(sqrt(3))`
    B
    `(sqrt(3))/(4)`
    C
    `sqrt(2)`
    D
    `(1)/(sqrt(3))`

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    Find the values of theta and p if the equation x cos theta+y sin theta=p is the normal form of the line sqrt3 x+y+2=0

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