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

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

The angles of elevation of the top of a tower from two points P and Q at distances m^(2) and n^(2) respectively,from the base and in the same straight line with it are complementary.The height of the tower is (mn)^(1/2) (b) mn^(1/2) (c) m^(1/2)n(d)mn

If the equation px^(2)-20xy+y^(2)+2gx+2fy+c=0 represents a pair of straight lines whose slopes are m and m^(2) ,then sum of all possible values of p is

If a/b = c/d =e/f = 4, then (m ^(2) a + n^(2) c + p ^(2) e )/( m ^(2) b + n ^(2) d + p ^(2) f )=?

A biard is at a point P(4m,-1m,5m) and sees two points P_(1) (-1m,-1m,0m) and P_(2)(3m, -1m,-3m) . At time t=0 , it starts flying in a plane of the three positions, with a constant speed of 2m//s in a direction perpendicular to the straight line P_(1)P_(2) till it sees P_(1) & P_(2) collinear at time t. Find the time t.

If the lines whose equations are y=m_1 x+ c_1 , y = m_2 x + c_2 and y=m_3 x + c_3 meet in a point, then prove that : m_1 (c_2 - c_3) + m_2 (c_3 - c_1) + m_3 (c_1 - c_2) =0

Find the equations of the straight lines , bisectors of the angles formed by the following pairs of lines y-b=(2m)/(1-m^(2))(x-a) and y-b=(2m')/(1-m' ^(2))(x-a)

If in an A.P., S_n=n^2p and S_m=m^2p , where S_r denotes the sum of r terms of the A.P., then S_p is equal to 1/2p^3 (b) m n\ p (c) p^3 (d) (m+n)p^2

Find the coordinates that the straight lines y=m_(1)x+c_(1),y=m_(2)x+c_(2) and y=m_(2)x+c_(3) may meet in a point.

For the equation 3x^(2)+px+3=0,p>0, if one of the root is square of the other,then p is equal to (2000,1M)(1)/(3)(b)1(c)3(d)(2)/(3)