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238. EXAMPLE If the normals at three poi...

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)

Text Solution

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`y=mx-2am-am^3`
`(am_1^2,-2am_1)(am_2^2,-2am_2)(am_3^2,-2am_3)`
`am^3+2am-mh+k=0`
`m_1+m_2+m_3=0`
`m_1m_2+m_1m_3+m_2m_3=(2a-h)/a`
`m_1m_2m_3=-k/a`
=SP*SQ*SR
`=(am_1^2+a)(am_2^2+a)(am_3^2+a)`
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