A point moves in the xy-plane such that the s | vedclass

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

Question

(B) Let the two mutually perpendicular lines be the coordinate axes $x=0$ and $y=0$.Let the point be $(x, y)$. The distances from these lines are $|x|

Vedclass · Accepted Answer

$25$

Vedclass · Answer

(B) Let the two mutually perpendicular lines be the coordinate axes $x=0$ and $y=0$.Let the point be $(x, y)$. The distances from these lines are $|x|$ and $|y|$.The given condition is $|x| + |y| = 5$.This equation represents a square with vertices at $(5, 0), (0, 5), (-5, 0),$ and $(0, -5)$.The length of the diagonal of this square is the distance between $(5, 0)$ and $(0, 5)$,which is $\sqrt{(5-0)^2 + (0-5)^2} = \sqrt{25 + 25} = \sqrt{50} = 5\sqrt{2}$.The area of a square with diagonal $d$ is given by $\frac{1}{2} d^2$.Area $= \frac{1}{2} 	imes (5\sqrt{2})^2 = \frac{1}{2} 	imes 50 = 25$ sq units.

$A$ point moves in the $xy$-plane such that the sum of its distances from two mutually perpendicular lines is always equal to $5$ units. The area (in sq units) enclosed by the locus of the point is

Similar Questions

$A$ body of mass $1\, kg$ is thrown upwards with a velocity $20\, m/s$. It momentarily comes to rest after attaining a height of $18\, m$. How much energy is lost due to air friction? $(g = 10\, m/s^2)$

How many $H$ atoms are present in $0.046 \, g$ of ethanol $(C_2H_5OH)$?

The $pH$ of $0.01 \ M$ solution of acetic acid is $5.0$. What are the values of $[H^{+}]$ and $K_a$ respectively?

If the equations $x^2+ax+b=0$ and $x^2+bx+a=0$ $(a \neq b)$ have a common root,then $a+b$ is equal to

What does an $ECG$ measure?

Vedclass Test Series

Exam Paper Generator

Online Exam Module