A line passing through the point $$P(1$$, $$2)$$ meets the line $$x+y=7$$ at the distance of $$3$$ units from P. Then the slope of this line satisfies the equation

Question

A line passing through the point $$P(1$$, $$2)$$ meets the line $$x+y=7$$ at the distance of $$3$$ units from P. Then the slope of this line satisfies the equation

Infinity Learn · Accepted Answer

An equation of line through (1$$, $$2) is y – $$2$$ $$=$$ $$m(x$$ – $$1)$$ A point on this line is of the form $$Q(x$$, mx – m $$+$$ $$2)$$. This point will lie on the line x $$+$$ y $$=$$ $$7$$ if $$x+mx$$−$$m+2=7$$⇒$$x=m+5m+1$$ As $$PQ=3$$,$$PQ2=9$$⇒$$(x$$−$$1)2+(mx$$−$$m)2=9$$⇒$$(x$$−$$1)21+m2=9$$⇒$$16m2+16=9m2+18m+9$$⇒$$7m2$$−$$18m+7=0$$⇒m satisfies the equation $$7x2$$−$$18x+7=0$$

A line passing through the point P(1, 2) meets the line $x + y = 7$ at the distance of 3 units from P. Then the slope of this line satisfies the equation

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A line passing through the point P(1, 2) meets the line x+y=7 at the distance of 3 units from P. Then the slope of this line satisfies the equation

Remember concepts with our Masterclasses.

Ready to Test Your Skills?

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A line passing through the point P(1, 2) meets the line $x + y = 7$ at the distance of 3 units from P. Then the slope of this line satisfies the equation