Two straight lines `(y-b)=m_1(x+a)` and `(y-b)=m_2(x+a)` are the tangents of `y^2=4a xdot` Prove `m_1m_2=-1.`

Two straight lines `(y-b)=m_1(x+a)` and `(y-b)=m_2(x+a)` are the tangents of `y^2=4a xdot` Prove `m_1m_2=-1.`

Monjur Alahi

4 views

2025-01-04 04:42

1 Answers

Salim Ahmed Kawsar

Clearly, both the lines pass through (-a,b), which is a point lying on the directrix of the parabola.
Thus, `m_(1)m_(2)=-1`, because tangents drawn from any point on the directrix are always mutually perpendicular.

4 views Answered 2023-02-05 15:29

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