If `2y + (1)/(2y) = l` and `2y - (1)/(2y) = m` , then `l^(2) - m^(2) = "______"`.

l and m are the lengths of the tangents from the origin and the point (9, -1) to the circle x^(2) + y^(2) + 18x - 2y + 32 = 0 . The value of 17(l^(2) + m^(2)) is equal to ________ .

l and m are the lengths of the tangents from the origin and the point (9, -1) to the circle x^(2) + y^(2) + 18x - 2y + 32 = 0 The value of 17(l^(2) + m^(2)) is equal to ________ .

If lx+ my = 1 is a normal to the hyperbola (x^(2))/(a^(2)) - (y^(2))/(b^(2)) = 1, "then" a^(2) m^(2) - b^(2) l^(2) =

Mention the condition under which the lines ( x - x _(1))/( l _(1)) = ( y - y _(1))/( m _(1)) = ( z - z _(1))/( n _(1)) and ( x - x _(2))/( l _(2)) = ( y-y _(2))/( m _(2)) = ( z - z _(2))/( n _(2)) will be perpendicular to each other.

Curve b^(2)x^(2) + a^(2)y^(2) = a^(2)b^(2) and m^(2)x^(2)- y^(2)l^(2) = l^(2)m^(2) intersect each other at right-angle if:

Curve b^(2)x^(2) + a^(2)y^(2) = a^(2)b^(2) and m^(2)x^(2)- y^(2)l^(2) = l^(2)m^(2) intersect each other at right-angle if:

l f y+b= m_(1) (x+ a) and y+b= m_(2) (x+a) are two tangents to y^(2) = 4ax , then show that m_(1)m_(2) = -1.

If y = e^(m cos^(-1) x) (1-x^2)y_2-xy_1 = m^2y

For the natural number m, n, if ( 1- y ) ^(m) (1 + y) ^( n) =1 + a _(1) y + a _(2) y ^(2) + ...+ a _( m + n) y ^( m +n) and a _(1) = a _(2) = 10, then the value of (m+n) is equal to :