If we reduce `3x+3y+7=0` to the form `xcosalpha+ysinalpha=p ,` then find the value of `pdot`

If the equation 3x + 3y + 5 = 0 is written in the form x cos alpha + y sin alpha = p , then the value of sin alpha + cos alpha is

If line 3x-a y-1=0 is parallel to the line (a+2)x-y+3=0 then find the value of adot

If the line y-sqrt(3)x + 3=0 cuts the parabola y^2=x + 2 at A and B, then find the value of PA.PB(where P=(sqrt(3),0)

Find the value of alpha and p if the equation xcosalpha+ysinalpha=p is the normal form of the line sqrt(3x)+y+2=0 .

If 2 is a zero of the polynomial p (x) = 2x ^(2) - 3x + 7a, then find the value of a.

The tangents to x^2+y^2=a^2 having inclinations alpha and beta intersect at Pdot If cotalpha+cotbeta=0 , then find the locus of Pdot

Find the locus of the middle point of the portion of the line xcosalpha+ysinalpha=p which is intercepted between the axes, given that p remains constant.

Line a x+b y+p=0 makes angle pi/4 with xcosalpha+ysinalpha=p ,p in R^+ . If these lines and the line xsinalpha-ycosalpha=0 are concurrent, then (a) a^2+b^2=1 (b) a^2+b^2=2 (c) 2(a^2+b^2)=1 (d) none of these

Show that the straight line xcosalpha+ysinalpha=p touches the curve x y=a^2, if p^2=4a^2cosalphasinalphadot