A straight line is such that the sum of the reciprocal of its intercepts on the axes is constant and equal to 'a'. Then the line passes through the point: A)(1,1) B)(a,0) C)(1/a,1/a) D)(0,a)

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justaguide | College Teacher | (Level 2) Distinguished Educator

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The general equation of a straight line is Ax + By + C = 0

Ax + By + C = 0

=> Ax + By = -C

=> `x/(-C/A) + y/(-C/B) = 1`

The x and y intercepts are -C/A and -C/B respectively.

In the given problem, the sum of the reciprocal of the intercepts on the axes of the line is constant and equal to 'a',

=> `-A/C + -B/C = a` ...(1)

Substituting the coordinates of the points that are given:

A. A + B + C = 0

This does not satisfy (1)

B. aA + 0 + C = 0

This does not satisfy (1)

C. A/a + B/a + C = 0

=> A/a + B/a = -C

=> -A/C + -B/C = a

This satisfies (1)

D. 0 + aB + C = 0

This does not satisfy (1)

Only the point (1/a, 1/a) lies on the given line.

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