If every point on the line (a1$$ – $$a2)x$$ $$+$$ $$(b1$$ – $$b2)y$$ $$=$$ c is equidistant from the points $$(a1$$, $$b1) and (a2$$, $$b2) then $$2c$$ $$=$$

Question

If every point on the line (a1$$ – $$a2)x$$ $$+$$ $$(b1$$ – $$b2)y$$ $$=$$ c is equidistant from the points $$(a1$$, $$b1) and (a2$$, $$b2) then $$2c$$ $$=$$

Infinity Learn · Accepted Answer

Let (h$$, $$k) be any point on the given line then           nh−$$a12+k$$−$$b12=h$$−$$a22+k$$−$$b22$$⇒ $$2a1$$−$$a2h+2b1$$−$$b2k=a12+b12$$−$$a22$$−$$b22$$⇒ $$a1$$−$$a2h+b1$$−$$b2k$$         $$=(1/2)a12+b12$$−$$a22$$−$$b22$$              (i)Since$$ $$(h$$, $$k) lies on the given line         $$a1$$−$$a2h+b1$$−$$b2k=c$$               (ii)Comparing$$ $$(i) and (ii) we get $$c=(1/2)a12+b12$$−$$a22$$−$$b22$$.

If every point on the line $(a_{1} - a_{2}) x + (b_{1} - b_{2}) y = c$ is equidistant from the points $(a_{1}, b_{1})$ and $(a_{2}, b_{2})$ then $2 c =$

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If every point on the line (a1 – a2)x + (b1 – b2)y = c is equidistant from the points (a1, b1) and (a2, b2) then 2c =

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If every point on the line $(a_{1} - a_{2}) x + (b_{1} - b_{2}) y = c$ is equidistant from the points $(a_{1}, b_{1})$ and $(a_{2}, b_{2})$ then $2 c =$