A line which makes an acute angle `theta` with the positive direction of the x-axis is drawn through the point `P(3,4)` to meet the line `x=6` at `R` and `y=8` at `Sdot` Then, (a) `P R=3sectheta` (b)`P S=4cosectheta` (c)`P R+P S=(2(3sintheta+4costheta))/(sin2theta)` (d)`9/((P R)^2)+(16)/((P S)^2)=1`

A line which the positive direction of x-axis is drawn through the point P(3, 4), to cut the curve y^2= 4x at Q and R . Show that the lengths of the segments PQ and PR are numerical values of the roots of the equation r^2sin^2theta+4r(2sintheta-costheta)+4=0

If sintheta,tantheta,costheta are in G.P. then 4sin^2theta-3sin^4theta+sin^6theta=?

Let P M be the perpendicular from the point P(1,2,3) to the x-y plane. If vec O P makes an angle theta with the positive direction of the z- axis and vec O M makes an angle phi with the positive direction of x- axis, w h e r eO is the origin and thetaa n dphi are acute angels, then a. costhetacosphi=1//sqrt(14) b. sinthetasinphi=2//sqrt(14) c. ""tanphi=2 d. tantheta=sqrt(5)//3

Let P M be the perpendicular from the point P(1,2,3) to the x-y plane. If vec O P makes an angle theta with the positive direction of the z- axis and vec O M makes an angle varphi with the positive direction of x- axis, w h e r eO is the origin and thetaa n dvarphi are acute angels, then a. costhetacosvarphi=1//sqrt(14) b. sinthetasinvarphi=2//sqrt(14) c. ""tanvarphi=2 d. tantheta=sqrt(5)//3

If sintheta,tantheta,costheta are in G.P. then 4sin^2theta-3sin^4theta+sin^6theta=_________

If the straight line drawn through the point P(sqrt3,2) and making an angle (pi)/(6) with the x-axis meets the line sqrt3x-4y+8=0 at Q, find the length of PQ.

If the tangent and normal to the ellipse x^2 + 4y^2 = 4 at point P (theta) meets the major axes in Q and R respectively, and QR = 3 , then (A) cos theta = 1 /sqrt(3) (B) cos theta= 1/3 (C) cos theta = 2/3 (D) costheta = (-2/(3)

A point R with x - coordinate 4 lies on the line segment joining the points P(2,-3,4) and Q(8, 0, 10) . The coordinates of R are

P Q R is a triangle in which P Q=P R and S is any point on the side P Q . Through S , a line is drawn parallel to Q R and intersecting P R at Tdot Prove that P S=P Tdot

A tangent is drawn to the parabola y^2=4a x at P such that it cuts the y-axis at Qdot A line perpendicular to this tangents is drawn through Q which cuts the axis of the parabola at R . If the rectangle P Q R S is completed, then find the locus of Sdot .