Question

Ax+by+c=0 intersects the x axis at a point

Answer 1

SOLUTION

TO DETERMINE

The point where the line Ax+by+c=0 intersects the x axis

EVALUATION

Here the given equation of the line is

$\sf{Ax + by + c = 0 \: \: \: ....(1)}$

Let the line intersects x axis at the point P

Since the line intersects x axis at the point P

So ordinate of P = 0

Let the coordinates of the point P = ( h, 0)

Since P is a point on the line given by Equation (1)

So we have

$\sf{Ah + (b \times 0) + c = 0 }$

$\sf{Ah = - c }$

$\displaystyle \implies \sf{h = - \frac{c}{A} }$

Hence the required coordinates of the point is

$\displaystyle \sf{ \bigg( - \frac{c}{A} \:, \: 0 \bigg) }$

FINAL ANSWER

The required coordinates of the point is

$\displaystyle \sf{ \bigg( - \frac{c}{A} \:, \: 0 \bigg) }$

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