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

The equation of the parabola whose vertex and focus lie on the axis of x at distances a and a_1 from the origin, respectively, is (a) y^2-4(a_1-a)x (b) y^2-4(a_1-a)(x-a) (c) y^2-4(a-a_1)(x-a) (d) none of these

Find the number of all three elements subsets of the set {a_1, a_2, a_3, a_n} which contain a_3dot

Prove that the value of each the following determinants is zero: |[a_1,l a_1+mb_1,b_1],[a_2,l a_2+mb_2,b_2],[a_3,l a_3+m b_3,b_3]|

If the lines a_1x+b_1y+1=0,\ a_2x+b_2y+1=0\ a n d\ a_3x+b_3y+1=0 are concurrent, show that the points (a_1, b_1),\ (a_2, b_2)a n d\ (a_3, b_3) are collinear.

Let A_1,A_2,....A_n be the vertices of an n-sided regular polygon such that , 1/(A_1A_2)=1/(A_1A_3)+1/(A_1A_4) . Find the value of n.

Let A B C be a triangle. Let A be the point (1,2),y=x be the perpendicular bisector of A B , and x-2y+1=0 be the angle bisector of /_C . If the equation of B C is given by a x+b y-5=0 , then the value of a+b is (a) 1 (b) 2 (c) 3 (d) 4

Find the first five terms of the following sequence . a_1 = 1 , a_2 = 1 , a_n = (a_(n-1))/(a_(n-2) + 3) , n ge 3 , n in N

If the intercepts made by tangent, normal to a rectangular x^2-y^2 =a^2 with x-axis are a_1,a_2 and with y-axis are b_1, b_2 then a_1,a_2 + b_1b_2=

If (b_2-b_1)(b_3-b_1)+(a_2-a_1)(a_3-a_1)=0 , then prove that the circumcenter of the triangle having vertices (a_1,b_1),(a_2,b_2) and (a_3,b_3) is ((a_(2+a_3))/2,(b_(2+)b_3)/2)

If the area of the circle is A_1 and the area of the regular pentagon inscribed in the circle is A_2, then find the ratio (A_1)/(A_2)dot