Three sides of a triangle have the equations

MATHEMATICS · Single correct · CBSE · Mathematics · Conic Sections · Conic Sections

Problem

Three sides of a triangle have the equations Lr≡y−mrx−cr=0;r=1,2,3L_r \equiv y - m_r x - c_r = 0; r = 1, 2, 3 . Then λL2L3+μL3L1+νL1L2=0\lambda L_2 L_3 + \mu L_3 L_1 + \nu L_1 L_2 = 0 , where λ≠0,μ≠0,ν≠0\lambda \neq 0, \mu \neq 0, \nu \neq 0 is the equation of circumcircle of triangle, if (1) λ(m2+m3)+μ(m3+m1)+ν(m1+m2)=0\lambda(m_2 + m_3) + \mu(m_3 + m_1) + \nu(m_1 + m_2) = 0 (2) λ(m2m3−1)+μ(m3m1−1)+ν(m1m2−1)=0\lambda(m_2 m_3 - 1) + \mu(m_3 m_1 - 1) + \nu(m_1 m_2 - 1) = 0 (3) Both (a) and (b) (4) None of the above

Related theory

Browse the problem library