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=4cos e ctheta` (c)`P R=+P S=(2(3sintheta+4costheta)/(sin2theta))` (d)`9/((P R)^2)+(16)/((P S)^2)=1`

The ratio in which the point Q(5,4,-6) divides the line joining the points P(3,2,-4) and R(9,8,-10) is

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

If P is a point (x ,y) on the line y=-3x such that P and the point (3, 4) are on the opposite sides of the line 3x-4y=8, then

Tangents drawn from point P to the circle x^(2)+y^(2)=16 make the angles theta_(1) and theta_(2) with positive x-axis. Find the locus of point P such that (tan theta_(1)-tan theta_(2))=c ( constant) .

theta is acute angle between the lines x^(2)-xy-6y^(2)=0 , then (2costheta+3sintheta)/(4sintheta+5costheta) is

If the line segment joining the point A(3,4) and B(14,3) meets the X-axis at P, then the ratio in which P divides the segment AB is......

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

Pair of lines through (1, 1) and making equal angle with 3x - 4y=1 and 12x +9y=1 intersect x-axis at P_1 and P_2 , then P_1,P_2 may be

A variable chord of the circle x^2+y^2=4 is drawn from the point P(3,5) meeting the circle at the point A and Bdot A point Q is taken on the chord such that 2P Q=P A+P B . The locus of Q is (a) x^2+y^2+3x+4y=0 (b) x^2+y^2=36 (c) x^2+y^2=16 (d) x^2+y^2-3x-5y=0