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प्रश्न
The perpendicular from the origin to a line meets it at the point (– 2, 9), find the equation of the line.
उत्तर
Suppose the perpendicular drawn from the origin on the line AB meets AB.
Slope of OP = `-("y"_2 - "y"_1)/("x"_2 - "x"_1)`
= `(9 - 0)/(-2 -0)`
= `-9/2`
But AB ⊥ OP
∴ Slope of AB= `- 1/("m"_1) = - 1/(-9/2) = 2/9`
Now the slope of AB is `2/9` and passes through P(−2, 9).
∴ equation of AB
y – y1 = m(x – x1)
i.e., y − 9 = `2/9 = ("x" + 2)`
or 9y – 81 = 2x + 4
or 2x – 9y + 85 = 0
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