If a line is moving between the coordinate ax | vedclass

Name: Exam Paper Generator | JEE NEET Paper Generator | Vedclass
Brand: Vedclass
Rating: 5 (35 reviews)

Question

(C) Let the intercepts of the line on the $x$-axis and $y$-axis be $a$ and $b$ respectively. The equation of the line is $\frac{x}{a} + \frac{y}{b} =

Vedclass · Accepted Answer

$x+y=6$

Vedclass · Answer

(C) Let the intercepts of the line on the $x$-axis and $y$-axis be $a$ and $b$ respectively. The equation of the line is $\frac{x}{a} + \frac{y}{b} = 1$.Given that the sum of the intercepts is $a + b = 12$,so $b = 12 - a$.The area of the triangle formed by the line with the coordinate axes is $A = \frac{1}{2}ab$.Substituting $b = 12 - a$,we get $A = \frac{1}{2}a(12 - a) = 6a - \frac{1}{2}a^2$.To find the maximum area,we differentiate $A$ with respect to $a$ and set it to zero:$\frac{dA}{da} = 6 - a = 0 \Rightarrow a = 6$.Since $a = 6$,then $b = 12 - 6 = 6$.The equation of the line is $\frac{x}{6} + \frac{y}{6} = 1$,which simplifies to $x + y = 6$.

If a line is moving between the coordinate axes such that the sum of the intercepts made by it on the coordinate axes is always $12$,then the equation of that line which forms a triangle of maximum area with the coordinate axes is

Similar Questions

The set of all values of $a$ for which the function $f(x) = (a^2 - 3a + 2) \left( \cos^2 \frac{x}{4} - \sin^2 \frac{x}{4} \right) + (a - 1)x + \sin 1$ does not possess critical points is

Let $a$ be a real number such that the function $f(x) = ax^2 + 6x - 15, x \in R$ is increasing in $(-\infty, \frac{3}{4})$ and decreasing in $(\frac{3}{4}, \infty)$. Then the function $g(x) = ax^2 - 6x + 15, x \in R$ has a:

Prove that the radius of the right circular cylinder of greatest curved surface area which can be inscribed in a given cone is half of that of the cone.

If $x=-1$ and $x=2$ are extreme points of $f(x)=\alpha \log |x|+\beta x^2+x$,then

What are the minimum and maximum values of the function $f(x) = x^5 - 5x^4 + 5x^3 - 10$?

Vedclass Test Series

Exam Paper Generator

Online Exam Module