If the equation of the locus of a point equidistant from the points `(a_(1),b_(1))and (a_(2),b_(2))` is `(a_(1)-a_(2))x + (b_(1) - b_(2)) y + c = 0 ` , then the value of c is

Find the equation of locus of point equidistant from the points (a_(1)b_(1)) and (a_(2),b_(2)) .

If the equation of the locus of a point equidistant from the points (a_1,b_1) and (a_2,b_2) is (a_1-a_2)x+(b_2+b_2)y+c=0 , then the value of C is

If the points (a_(1),b_(1))m(a_(2),b_(2))" and " (a_(1)-a_(2),b_(2)-b_(2)) are collinear, then prove that a_(1)/a_(2)=b_(1)/b_(2)

The two points on the line x+y=4 that lies at a unit perpendicular distance from the line 4x+3y=10 are (a_(1), b_(1)) and (a_(2), b_(2)) then a_(1)+b_(1)+a_(2)+b_(2) is equal to (a) 5 (b) 6 (c) 7 (d) 8

Let A = {a_(1), b_(1), c_(1)} and B = {a_(2), b_(2)} (i) A xx B (ii) B xx B

If the lines x=a_(1)y + b_(1), z=c_(1)y +d_(1) and x=a_(2)y +b_(2), z=c_(2)y + d_(2) are perpendicular, then

If the tangent and normal at a point on rectangular hyperbola cut-off intercept a_(1), a_(2) on x-axis and b_(1), b_(2) on the y-axis, then a_(1)a_(2)+b_(1)b_(2) is equal to :

Statement - 1 : For the straight lines 3x - 4y + 5 = 0 and 5x + 12 y - 1 = 0 , the equation of the bisector of the angle which contains the origin is 16 x + 2 y + 15 = 0 and it bisects the acute angle between the given lines . statement - 2 : Let the equations of two lines be a_(1) x + b_(1) y + c_(1) = 0 and a_(2) x + b_(2) y + c_(2) = 0 where c_(1) and c_(2) are positive . Then , the bisector of the angle containing the origin is given by (a_(1) x + b_(1) y + c_(1))/(sqrt(a_(2)^(2) + b_(1)^(2))) = (a_(2) x + b_(2)y + c_(2))/(sqrt(a_(2)^(2) + b_(2)^(2))) If a_(1) a_(2) + b_(1) b_(2) gt 0 , then the above bisector bisects the obtuse angle between given lines .

Let (1 + x^(2))^(2) (1 + x)^(n) = a_(0) + a_(1) x + a_(2) x^(2) + … if a_(1),a_(2) " and " a_(3) are in A.P , the value of n is

a_(1), a_(2),a_(3) in R - {0} and a_(1)+ a_(2)cos2x+ a_(3)sin^(2)x=0 " for all " x in R then (a) vectors veca=a_(1) hati+ a_(2) hatj + a_(3) hatk and vecb = 4hati + 2hatj + hatk are perpendicular to each other (b)vectors veca=a_(1) hati+ a_(2) hatj + a_(3) hatk and vecb = hati + hatj + 2hatk are parallel to each each other (c)if vector veca=a_(1) hati+ a_(2) hatj + a_(3) hatk is of length sqrt6 units, then on of the ordered trippplet (a_(1), a_(2),a_(3)) = (1, -1,-2) (d)if 2a_(1) + 3 a_(2) + 6 a_(3) = 26 , " then " |veca hati + a_(2) hatj + a_(3) hatk | is 2sqrt6