Math, asked by archana2025, 1 year ago

Let P (x , y ) be any point on the line joining the points A (a,0) and B (0,b ) Show that x /a + y/b = 1

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Answers

Answered by Anonymous

Answer:

Step-by-step explanation:

Given that P(x,y) be any point on the straight line AB cutsoff intercepts a and b on x-axis at A(a,0) and y-axis at B(0,b) .

∴ Slope of the straight line AB = -b/a

Then the equation of straight line by the slope - intercept form

⇒ y = (-b/a) x + b

⇒ y / b = (-1/a) x + 1

⇒ x / a + y / b = 1.

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Answered by arjun6068

answers · Mathematics

Best Answer

∵ the points P(x,y), A(a,0) and B(0,b) are collinear

∴ (slope of AP) = (slope of AB)

∴ (y-0) / (x-a) = (b-0) / (0-a)

∴ y / (x-a) = -b / a

∴ ay = -b(x-a)

∴ ay = -bx + ab

∴ bx + ay = ab

∴ (bx+ay) / (ab) = 1

∴ [bx / (ab)] + [ay / (ab)] = 1

∴ ( x/a ) + ( y/b ) = 1

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