If the tangent and normal to a rectangular hyperbola cut off intercepts `a_(1)` and `a_(2)` on one axis and `b_(1)` and `b_(2)` on the other, then

If the tangent and normal to the rectangular hyperbola xy=16 at point (8,2) cut off intercepts a_(1),a_(2) on the x axis and b_(1)b_(2) on the y axis then a_(1)a_(2)+b_(1)b_(2)+7//2 equals

If the tangent and the normal to a rectangular hyperbola xy = c^(2) , at a point , cuts off intercepts a_(1)" and " a_(2) on the x- axis and b_(1) b_(2) on the y- axis, then a_(1)a_(2) + b_(1) b_(2) is equal to

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 normal to the hyperbola x^(2) - y^(2) = 4 at a point cut off intercepts a_(1) and a^(2) respectively on the x-axis, and b_(1) and b_(2) respectively on the y-axis, then the value of a_(1)a_(2) + b_(1)b_(2) is

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 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_(1)b_(2)=

Let a and b be positive real numbers such that a gt 1 and b lt a . Let be a point in the first quadrant that lies on the hyperbola (x^(2))/(a^(2)) - (y^(2))/(b^(2)) = 1 . Suppose the tangent to the hyperbola at P passes through the oint (1,0) and suppose the normal to the hyperbola at P cuts off equal intercepts on the coordinate axes . Let Delta denote the area of the triangle formed by the tangent at P , the normal at P and the x - axis . If a denotes the eccentricity of the hyperbola , then which of the following statements is/are TRUE ?

If vec P = a_(1) hati +a_(2) hatj and vec Q =b_(1) hati+b_(2)hatj are perpendicular to each other, then

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