Question

$\huge{\underline{\tt{Question:-}}}$
P(a,b) is mid-point of a line segment between axes. Show that equation of the line x/a+y/b=2.

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Answer 1

Question :----

• P(a,b) is mid-point of a line segment between axes. Show that equation of the line x/a+y/b=2.

solution :------

Let equation of line is

x/h + y/k = 1--------------- Equation (1)

here, h and k are intercepts made by the line on x-axis and y-axis respectively.

now,

A/q,

P(a, b) is the midpoint of (h,0) and (0,k) .

Use formula,

Midpoint of (x1, y1) and (x2, y2) is [(x1 + x2)/2 , (y1 + y2)/2 ]

So,

→ a = ( 0 + h)/2

→ a = h/2

→ h = 2a

b = (k + 0)/2

→ b = k/2

→ k = 2b

now, put this values in equation (1),

x/(2a) + y/(2b) = 1

x/a + y/b = 2

Hence Proved .......

#BAL

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Answer 2

The equation which comes after proving I.e:-

Let the coordinates of A and B be (0, y) and (x, 0) respectively.

Since P (a, b) is the mid-point of AB,

Thus, the respective coordinates of A and B are (0, 2b) and (2a, 0).

The equation of the line passing through points (0, 2b) and (2a, 0) is

On dividing both sides by ab, we obtain

x/a+y/b=2.

Thus,the equation of the line is x/a+y/b=2.

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