Question

Find the equations of the straight line which make intercepts whose sum is 5 and product is 6

Answer 1

SOLUTION

TO DETERMINE

The equations of the straight line which make intercepts whose sum is 5 and product is 6

EVALUATION

Let the required equation of the line is

$\displaystyle \sf{ \frac{x}{a} + \frac{y}{b} = 1 }$

Where x intercept = a and y - intercept = b

So by the given condition

a + b = 5 - - - - - - (1)

ab = 6 - - - - - - - (2)

From Equation 1 and Equation 2 we get

$\displaystyle \sf{ a(5 - a) = 6 }$

$\displaystyle \sf{ \implies \: {a}^{2} - 5a + 6 = 0 }$

$\displaystyle \sf{ \implies \: {a}^{2} - 3a - 2a+ 6 = 0 }$

$\displaystyle \sf{ \implies \: (a - 3)(a - 2)= 0 }$

$\displaystyle \sf{ \implies \: a = 3 \: \:, \: 2 }$

Now a = 3 gives b = 2

a = 2 gives b = 3

Hence there exists two lines

Hence the required equation of the lines are

$\displaystyle \sf{ \frac{x}{3} + \frac{y}{2} = 1 }$

And

$\displaystyle \sf{ \frac{x}{2} + \frac{y}{3} = 1 }$

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