The lines `y=m_1x ,y=m_2xa n dy=m_3x` make equal intercepts on the line `x+y=1.` Then (a) `2(1+m_1)(1+m_3)=(1+m_2)(2+m_1+m_3)` (b)`(1+m_1)(1+m_3)=(1+m_2)(1+m_1+m_3)` (c)`(1+m_1)(1+m_2)=(1+m_3)(2+m_1+m_3)` (d)`2(1+m_1)(1+m_3)=(1+m_2)(1+m_1+m_3)`

If y+3=m_1(x+2) and y+3=m_2(x+2) are two tangents to the parabola y^2=8x , 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

Two straight lines (y-b)=m_1(x+a) and (y-b)=m_2(x+a) are the tangents of y^2=4a x. Prove m_1m_2=-1.

If three lines whose equations are y = m_(1) x + c_(1) , y = m_(2) x + c_(2) " and " m_(3) x + c_(3) are concurrent, then show that m_(1) (c_(2) - c_(3)) + m_(2) (c_(3) - c_(1)) + m_(3) (c_(1) - c_(2)) = 0 .

If the lines y = 3x + 1 and 2y = x + 3 are equally inclined to the line y = mx + 4, ((1)/(2) lt m lt 3) , then the values of m are

The value of ^n C_1+^(n+1)C_2+^(n+2)C_3++^(n+m-1)C_m is equal to (a) ^m+n C_(n-1) (b) ^m+n C_(n-1) (c) ^mC_(1)+^(m+1)C_2+^(m+2)C_3++^(m+n-1) (d) ^m+1C_(m-1)

Find the GCD of the following : a^(m+1) , a ^(m+2) , a^(m+3)

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

Show that the area of the triangle formed by the lines y = m_(1) x + c_(1) , y = m_(2) x + c_(2) " and " x = 0 " is " ((c_(1) - c_(2))^(2))/(2|m_(1) - m_(2)|)

Three sided of a triangle have equations L_1-=y-m_i x=o; i=1,2a n d3. Then L_1L_2+lambdaL_2L_3+muL_3L_1=0 where lambda!=0,mu!=0, is the equation of the circumcircle of the triangle if 1+lambda+mu=m_1m_2+lambdam_2m_3+lambdam_3m_1 m_1(1+mu)+m_2(1+lambda)+m_3(mu+lambda)=0 1/(m_3)+1/(m_1)+1/(m_1)=1+lambda+mu none of these