Home
Class 12
MATHS
If (mi,1/mi),i=1,2,3,4 are concyclic poi...

If (m_i,1/m_i),i=1,2,3,4 are concyclic points then the value of `m_1m_2m_3m_4` is

Text Solution

Verified by Experts

Let the points `(m_(i),(1)/(m_(i))),i = 1,2,3,4`
lie on a circle `x^(2) | y^(2)+2gx+2fy+c-0`.
Then, `m_(i)^(2)+(1)/(m_(i)^(2))+2gm_(i)+(2f)/(m_(i))+c=0`,
Since, `m_(i)^(4)+2gm_(i)^(3)+cm_(i)^(2)+2fm_(i)+1=0, i=1,2,3,4`
`rArr m_(1), m_(2), m_(3) and m_(4)` are the roots of the equation
`m^(4)+2gm^(3)+cm^(2)+2fm+1=0`
`rArr" " m_(1)m_(2)m_(3)m_(4)=(1)/(1)=1`
Promotional Banner

Topper's Solved these Questions

  • CIRCLE

    IIT JEE PREVIOUS YEAR|Exercise Topic 1 Integer Answer Type Questions|2 Videos

  • CIRCLE

    IIT JEE PREVIOUS YEAR|Exercise Topic 1 Paragraph Based Questions|2 Videos

  • CIRCLE

    IIT JEE PREVIOUS YEAR|Exercise Topic 1True/False|1 Videos

  • BINOMIAL THEOREM

    IIT JEE PREVIOUS YEAR|Exercise Topic 2 Properties of Binomial Coefficent Objective Questions I (Only one correct option) (Analytical & Descriptive Questions )|8 Videos

  • COMPLEX NUMBERS

    IIT JEE PREVIOUS YEAR|Exercise TOPIC 5 DE-MOIVRES THEOREM,CUBE ROOTS AND nth ROOTS OF UNITY (INTEGER ANSWER TYPE QUESTION)|1 Videos

Similar Questions

Explore conceptually related problems

If (m_(-)i,1/m_(-)i),i=1,2,3,4 are concyclic points then the value of m_(1)m_(2)m_(3)m_(4) is

If (m_(i),(1)/(m_(i))),i=1,2,3,4 are concyclic points,then the value of m_(1)m_(2)m_(3)m_(4) is

If (m_i , 1/m_i), i= 1, 2, 3, 4 are four distinct points on a circle, show that m_1 m_2 m_3 m_4 = 1

If m^2-4m+1=0 then the value of (m^3+1/m^3) is:

Two tangents to the hyperbola (x^(2))/(a^(2))-(y^(2))/(b^(2))=1 having m_(1) and m_(2) cut the axes at four concyclic points.Fid the value of m_(1)m_(2)

If |[3,m],[4,7]|=1 , then the value of m is:

If ((1+i)/(1-i))^(m)=1, then find the least integral value of m

If ((1+i)/(1-i))^(m)=1 then find the least integral value of m

If ((1+i)/(1-i))^(m)=1, then find the least positive integral value of m.