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A line cuts the x-axis at A (7, 0) and t...

A line cuts the x-axis at `A (7, 0)` and the y-axis at `B(0, - 5)` A variable line PQ is drawn perpendicular to AB cutting the x-axis in P and the y-axis in Q. If AQ and BP intersect at R, find the locus of R.

Text Solution

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From the figure in `Delta ABQ`,
`APbotBQ,PQbotAB`

Then, we have `Bpbot AQ` (as the altitudes of triangle are concurrent). Hence,
`BRbotAR`
or `(k-0)/(h-7)xx(k+5)/(h-0)=-1`
Therefore, equation of the locus of R is `x^2+y^2-7x+5y=0` .
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