Two straight lines pass through the fixed points `(+-a, 0)` and have slopes whose products is `pgt0` Show that the locus of the points of intersection

Question

Two straight lines pass through the fixed points `(+-a, 0)` and have slopes whose products is `pgt0` Show that the locus of the points of intersection

Two straight lines pass through the fixed points `(+-a, 0)` and have slopes whose products is `pgt0` Show that the locus of the points of intersection of the lines is a hyperbola.

Monjur Alahi

7 views

2025-01-04 04:42

1 Answers

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Salim Ahmed Kawsar · Accepted Answer · 2023-02-05T15:29:48+06:00

Salim Ahmed Kawsar

Let the equation of the lines be
`y=m_(1)(x-a)`
`and y=m_(2)(x+a)`
`therefore" "m_(1)m_(2)=p`
`therefore" "y^(2)=m_(1)m_(2)(x^(2)-a^(2))=p(x^(2)-a^(2))`
Hence, the locus of the points of intersection is
`y^(2)=p(x^(2)-a^(2))`
`" "px^(2)-y^(2)=pa^(2)`
which is a hyperbola.

7 views Answered 2023-02-05 15:29