Question

derive the equation of a straight line in intercept from

Answer 1

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Answer 2

Hey frnd here is ur query...

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intercept from

(x/a)+(y/b)=1

Proof

Let P(x, y) be any point on the line AB. Draw PQ perpendicular on OX and PR perpendicular on OX. Then, join the points O and P. Now, PQ = y, OQ = x.

Clearly, we see that

Area of the ∆OAB = Area of the ∆OPA + Area of the ∆OPB

⇒ ½ OA ∙ OB = ½ ∙ OA ∙ PQ + ½ ∙ OB ∙ PR

⇒ ½ a ∙ b = ½ ∙ a ∙ y + ½ ∙ b ∙ x

⇒ ab = ay + bx

⇒ abababab = ay+bxabay+bxab, dividing both sides by ab

⇒ 1 = ayabayab + bxabbxab

⇒ 1 = ybyb + xaxa

⇒ xaxa + ybyb = 1, which is the equation of the line in the intercept form.

The equation xaxa + ybyb = 1 is the satisfied by the co-ordinates of any point P lying on the line AB.

Therefore, xaxa + ybyb = 1 represent the equation of the straight line AB.

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hope this will help you..