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

If the points ( a_1,b_1),(a_2,b_2) and (a_1+a_2,b_1+b_2) are collinear ,show that a_1b_2=a_2b_1 .

If A_1,B_1,C_1, are respectively, the cofactors of the elements a_1, b_1,c_1, of the determinant "Delta"=|[a_1b_1c_1][a_2b_2c_2][a_3b_3c_3]|,"Delta"!=0 , then the value of |[B_2C_2][B_3C_3]| is equal to a. a1^2Δ b. a_1Δ c. a_1^2Δ d. a1 2^2Δ

Let A_r ,r=1,2,3, , be the points on the number line such that O A_1,O A_2,O A_3dot are in G P , where O is the origin, and the common ratio of the G P be a positive proper fraction. Let M , be the middle point of the line segment A_r A_(r+1.) Then the value of sum_(r=1)^ooO M_r is equal to (a) (O A_1(O S A_1-O A_2))/(2(O A_1+O A_2)) (b) (O A_1(O A_2+O A_1))/(2(O A_1-O A_2) (c) (O A_1)/(2(O A_1-O A_2)) (d) oo

If tangent at point P(a,b) to the curve x^3+y^3=c^3 meet the curve agins at Q(a_1, b_1) then (a_1)/a +b_1/b=

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_1-a)(x-a) (d) n o n e

Find the condition so that the two equations a_1 x^2+b_1 x+c_1=0 and a_2 x^2+b_2 x+c_2=0 will have a common root.

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)

Express the square of |{:(a_1,b_1,0),(a_2,b_2,0),(a_3,b_3,0):}| as a third order determinant ,what is the value of this determinant ?

Consider the sequence defined by a_n=a n^2+b n+c dot If a_1=1,a_2=5,a n da_3=11 , then find the value of a_(10)dot

Let a_1,a_2,a_3,.......a_11 be real number satisfying a_1=15,27-2a_2gt0 anda_k=2a_(k-1)-a_(k-2) for k=3,4,.....11. If (a_1^2+a_2^2+......a_11^2)/11=90, then the value of (a_1 +a_2+.....a_11)/11 is equal to