If the tangent and normal to `xy=c^2` at a given point on it cut off intercepts `a_1, a_2` on one axis and `b_1, b_2` on the other axis, then `a_1 a_2 + b_1 b_2 `=
(A) `-1` (B) `1` (C) `0` (D) `a_1 a_2 b_1 b_2`

If the tangent and the normal to x^2-y^2=4 at a point cut off intercepts a_1,a_2 on the x-axis respectively & b_1,b_2 on the y-axis respectively. Then the value of a_1a_2+b_1b_2 is equal to:

If the intercepts made by tangent, normal to a rectangular hyperbola 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=

The ratio in which the line segment joining points A(a_1,\ b_1) and B(a_2,\ b_2) is divided by y-axis is (a) -a_1: a_2 (b) a_1: a_2 (c) b_1: b_2 (d) -b_1: b_2

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 and A_2 are two AMs between a and b then (2A_1 -A_2) (2A_2 - A_1) =

y^2=21-x x=5 The solutions to the system of equation above are (a_1,b_1) and (a_2,b_2) . What are the values of b_1 and 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_1-b_2)y+c=0 , then the value of c is a a2-a2 2+b1 2-b2 2 sqrt(a1 2+b1 2-a2 2-b2 2) 1/2(a1 2+a2 2+b1 2+b2 2) 1/2(a2 2+b2 2-a1 2-b1 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 origin lies in the acute angle between the lines a_1 x + b_1 y + c_1 = 0 and a_2 x + b_2 y + c_2 = 0 , then show that (a_1 a_2 + b_1 b_2) c_1 c_2 lt0 .

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 find the value of c .