If the equations `y=m x+c` and `xcosalpha+ysinalpha=p` represent the same straight line, then (a)`p=csqrt(1+m^2)` (b) `c=psqrt(1+m^2)` (c)`c p=sqrt(1+m^2)` (d) `p^2+c^2+m^2=1`

If cos25^0+sin25^0=p , then cos50^0 is (a) sqrt(2-p^2) (b) -sqrt(2-p^2) (c) psqrt(2-p^2) (d) -psqrt(2-p^2)

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 .

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

If the straight line xcosalpha+ysinalpha=p touches the curve (x^2)/(a^2)+(y^2)/(b^2)=1 , then prove that a^2cos^2alpha+b^2sin^2alpha=p^2dot

The two circles which pass through (0,a)a n d(0,-a) and touch the line y=m x+c will intersect each other at right angle if (A) a^2=c^2(2m+1) (B) a^2=c^2(2+m^2) (C) c^2=a^2(2+m^2) (D) c^2=a^2(2m+1)

If y=m_1x+c and y=m_2x+c are two tangents to the parabola y^2+4a(x+a)=0 , then

If one of the lines of m y^2+(1-m^2)x y-m x^2=0 is a bisector of the angle between the lines x y=0 , then m is (a) 1 (b) 2 (c) -1/2 (d) -1

If z=x+i y , then he equation |(2z-i)/(z+1)|=m represents a circle, then m can be (a) 1/2 b. 1 c. 2 d. 3

Choose the odd one out (1) y^(2) = 4ax (2) c= a/m (3) c^(2) = a^(2(1+m^(2))) (4) (a/m^(2) , (2a)/m)