Search any question & find its solution
Question:
Answered & Verified by Expert
If $a$ is a parameter then an equation of a family of lines having the sum of the intercepts on axes equal to 7 is
Options:
Solution:
2160 Upvotes
Verified Answer
The correct answer is:
$a y=(7-a)(a-x)$
Since, equation of family of lines is $\frac{x}{a}+\frac{y}{b}=1 \ldots$ (i)
Sum of intercepts $=a+b=7$ (given)
$\Rightarrow \quad b=7-a$
Substitute $b=7-a$ in Eq. (i), we get
$$
\begin{gathered}
\frac{x}{a}+\frac{y}{7-a}=1 \\
\Rightarrow(7-a) x+a y=a(7-a) \Rightarrow a y=(7-a)(a-x)
\end{gathered}
$$
Sum of intercepts $=a+b=7$ (given)
$\Rightarrow \quad b=7-a$
Substitute $b=7-a$ in Eq. (i), we get
$$
\begin{gathered}
\frac{x}{a}+\frac{y}{7-a}=1 \\
\Rightarrow(7-a) x+a y=a(7-a) \Rightarrow a y=(7-a)(a-x)
\end{gathered}
$$
Looking for more such questions to practice?
Download the MARKS App - The ultimate prep app for IIT JEE & NEET with chapter-wise PYQs, revision notes, formula sheets, custom tests & much more.