If `(m_i,1/m_i),i=1,2,3,4` are concyclic points then the value of `m_1m_2m_3m_4` is
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Given that `(m_(i),1//m),m_(i)gt0,i=1,2,3,4` are four distinct points on a circle. Let the equation of circel be `x^(2)+y^(2)+2gx+2fy+c=0` As the point `(m,1//m)` lies on it, we have `m^(2)+(1)/(m^(2))+2gm+(2f)/(m)+c=0` or `m^(4)+2gm^(3)+cm(2)+2fm+1=0` Since `m_(1),m_(2),m_(3)` and `m_(4)` are the roots of this equation, the products of roots is 1,i.e., `m_(1),m_(2),m_(3),m_(4)=1`
If ( m_r , 1/m_r ) where r=1,2,3,4, are four pairs of values of x and y that satisfy the equation x^2+y^2+2gx+2fy+c=0 , then the value of m_1. m_2. m_3. m_4 is a. 0 b. 1 c. -1 d. none of these
If ((1+i)/(1-i))^(m)=1 , then find the least positive integral value of m.
The area of the triangle with vertices (-1,m),(3,4) (m-2,m) is 1" sq.units , " then find the value of m.
If m + (1)/(m) = sqrt3 , then find the simpliest value of (i) m^(2) + (1)/(m^(2)) and (ii) m^(3) + (1)/(m^(3)) :
If I_(m)=int_(1)^(e )(log_(e)x)^(m)dx , then the value of (I_(m)+mI_(m-1)) is -
STATEMENT 1: Let m be any integer. Then the value of I_m=int_0^pi(sin2m x)/(sinx)dx is zero. STATEMENT 2 : I_1=I_2=I_3=I_m
If m, n in R , then the value of I(m,n)=int_(0)^(1) t^(m)(1+t)^(n)dt is -
If the straight line joining the points (4, -3, 2) and (3, -1, 5) is perpendicular to the straight line joining the points (m, -2, 1) and (7, 3, -2), then the value of m is -
