Let the latus ractum of the hyperbola `(x^(2))/(9)-(y^(2))/(b^(2))=1` subtend an angle of `(pi)/(3)` at the centre of the hyperbola.If `b^(2)` is equal to `(l)/(m)(1+sqrt(n))` ,where "l" and "m" are co-prime numbers,then `l^(2)+m^(2)+n^(2)` is equal to

If l, m, n denote the side of a pedal triangle, then (l)/(a ^(2))+(m)/(b^(2))+(n)/(c ^(2)) is equal to

If a+b=1,a^(2)+b^(2)=2 and given that a^(7)+b^7=(m)/(n) where m & n are co-primes. Find m+n

If one root of the equation lx^(2)+mx+n=0 is (9)/(2) equal to (l,m and n are positive integers) and (m)/(4n)=(l)/(m), then l+n is equal to

L_(1):x+y=0 and L_(2)*x-y=0 are tangent to a parabola whose focus is S(1,2). If the length of latus-rectum of the parabola can be expressed as (m)/(sqrt(n)) (where m and n are coprime then find the value of (m+n)

Let l_(1) be the length of the latus rectum of the parabola 9x^(2)-6x+36y+19=0. Let l_(2), be the length of the latus rectum of the hyperbola 9x2-16y^(2)-18x-32y-151=0. Let n be the unit digit in the product of l_(1) and l_(2) The number of terms in the binomial expansion of (1+x)^(n) is

If x=4(l)/(1+l^(2)) and y=(2-2l^(2))/(1+l^(2)) wherel' is a parameter and range of f(x,y)=x^(2)-xy+y^(2) is[a,b ] then (a+b) is equal to

The point of intersection of tangents drawn to the hyperbola (x^(2))/(a^(2))-(y^(2))/(b^(2))=1 at the points where it is intersected by the line lx+my+n=0, is (A) ((-a^(2)l)/(n),(b^(2)m)/(n))(B)((-a^(2)l)/(m),(b^(2)n)/(m))(C)((a^(2)l)/(m),(-b^(2)n)/(m))(D)((a^(2)l)/(m),(b^(2)n)/(m))

lim_(x rarr2)[(x-2)/(x^(2)-4)-(1)/(x^(3)-3x^(2)+x)]=(1)/(m) where l and m are mutually prime then the value of (l+m)

Let L be the line of intersection of the planes 2x+3y+z=1 and x+3y+2z=2. If L makes an angle alpha with the positive x-axis,then cos alpha equals a.(1)/(2) b.1 c.(1)/(sqrt(2)) d.(1)/(sqrt(3))