A stick of length l rests against the floor a | vedclass

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

Question

(B) Let the coordinates of the ends of the stick be $(a, 0)$ on the floor and $(0, b)$ on the wall. The length of the stick is $l$,so $a^2 + b^2 = l^2

Vedclass · Accepted Answer

Circle

Vedclass · Answer

(B) Let the coordinates of the ends of the stick be $(a, 0)$ on the floor and $(0, b)$ on the wall. The length of the stick is $l$,so $a^2 + b^2 = l^2$.Let the middle point of the stick be $(h, k)$.By the midpoint formula,$h = \frac{a+0}{2} = \frac{a}{2}$ and $k = \frac{0+b}{2} = \frac{b}{2}$.This gives $a = 2h$ and $b = 2k$.Substituting these into the equation $a^2 + b^2 = l^2$,we get $(2h)^2 + (2k)^2 = l^2$.$4h^2 + 4k^2 = l^2 \Rightarrow h^2 + k^2 = \frac{l^2}{4}$.Replacing $(h, k)$ with $(x, y)$,the locus is $x^2 + y^2 = \left(\frac{l}{2}\right)^2$,which represents a circle.

$A$ stick of length $l$ rests against the floor and a wall of a room. If the stick begins to slide on the floor,then the locus of its middle point is

Similar Questions

The locus of the point of intersection of the tangents to the circle $x^2+y^2=16$,such that the angle between them is $60^{\circ}$,is

Any circle passing through the point of intersection of the lines $x + \sqrt{3}y = 1$ and $\sqrt{3}x - y = 2$ intersects these lines at points $P$ and $Q$. The angle subtended by the arc $PQ$ at its centre is- ............. $^o$

If $P$ is a point such that the ratio of the square of the lengths of the tangents from $P$ to the circles $x^2+y^2+2x-4y-20=0$ and $x^2+y^2-4x+2y-44=0$ is $2:3$,then the locus of $P$ is a circle with centre :

The locus of the point of intersection of perpendicular tangents to the circle $x^{2}+y^{2}=16$ is

Vedclass Test Series

Exam Paper Generator

Online Exam Module