Prove that a point can be found which is at the same distance from each of the four points :`(a m_1, a/(m_1))*(a m_2, a/(m_2))*(a m_3, a/(m_3))"and"(a/(m_1m_2 m_3), a m_1m_2m_3)`

238. EXAMPLE If the normals at three points P, Q and R in a s be the focus, meet point O and prove that SP. SQ. SR a SO As in the previous question we know that the normals a the points (ami, am 1), (am am2) and (am3, 2am3) meet in the point (h k), if m1 1m2 1m3 0 2a -h m2m3 m3m1 m1m2 (2)

In the figure, m_(1) is at rest, find the relation among m_(1),m_(2) and m_(3) ? .

Prove that the three lines from O with direction cosines l_1, m_1, n_1: l_2, m_2, n_2: l_3, m_3, n_3 are coplanar, if l_1(m_2n_3-n_2m_3)+m_1(n_2l_3-l_2n_3)+n_1(l_2m_3-l_3m_2)=0

Prove that the lengths of the perpendiculars from the points (m^(2),2m),(mm',m+m') and (m^(2),2m') to the line x+y+1=0 are in GP.