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 a line is drawn through a point A(3,4) to cut the circle x^(2)+y^(2)=4 at P and Q then AP .AQ=

A value of theta satifying 4costheta sintheta - 2sintheta =0 is

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

Show that that the radii of the three escribed circles of a triangle are the roots of the equation x^3-x^2(4R+r)+xs^2-rs^2=0

A tangent to the circle x^(2)+y^(2)=1 through the point (0, 5) cuts the circle x^(2)+y^(2)=4 at P and Q. If the tangents to the circle x^(2)+y^(2)=4 at P and Q meet at R, then the coordinates of R are

Find the least and greatest values of the distance of the point (costheta,sintheta),theta in R , from the line 3x-4y+10=0.

Find the least and greatest values of the distance of the point (costheta,sintheta),theta in R , from the line 3x-4y+10=0.

sintheta=(1)/(sqrt(2)) ,then find the value of 3sin ^(2)theta-4sin^(3)theta*costheta .

The solution of the equation cos^2theta-2costheta=4sintheta-sin2theta where theta in [0,pi] is

If the straight line through the point P(4,4) makes an angle pi/4 with x-axis and meets the line 12 x + 5 y + 10 = 0 at Q, Then the length of PQ is :