The area of triangle formed by the coordinate axis and a line is 15/2 square units and the length of it's hypotenuse is √34 units. Find the equation of the line.
Answers
Answer:
It is given that ,The area of the triangle formed by the coordinate axes and a line is 6 square units .
We get any one of two right angled triangles shown above :
case 1:
The line intersects x - axis at A( a,0 )= (3,0) and
y - axis at B(0,b) = (0,4)
X - intercept = a = 3 ,
y - intercept = b = 4,
\underline { \pink { Two \: intercept \:form : }}Twointerceptform:
\boxed { \orange { \frac{x}{a} + \frac{y}{b} = 1 }}ax+by=1
$$\begin{lgathered}Substituting \: the \: values , we \: get \\Equation \: of \:the \:line :\\\end{lgathered}$$
$$\frac{x}{3} + \frac{y}{4} = 1\: ---(1)$$
case 2:
The line intersects x - axis at P( a,0 )= (4,0) and
y - axis at Q(0,b) = (0,3)
X - intercept = a = 4 ,
y - intercept = b = 3,
$$\begin{lgathered}Substituting \: the \: values , we \: get \\Equation \: of \:the \:line :\\\end{lgathered}$$
$$\frac{x}{4} + \frac{y}{3} = 1\: ---(2)$$
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