A rod of length 2l slides with its ends on tw | vedclass

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

Question

(A) Let the two perpendicular lines be the coordinate axes $OX$ and $OY$. Let the ends of the rod be $A(0, a)$ on the $y$-axis and $B(b, 0)$ on the $x

Vedclass · Accepted Answer

$x^2+y^2=l^2$

Vedclass · Answer

(A) Let the two perpendicular lines be the coordinate axes $OX$ and $OY$. Let the ends of the rod be $A(0, a)$ on the $y$-axis and $B(b, 0)$ on the $x$-axis.The length of the rod is $AB = 2l$. By the distance formula,$\sqrt{a^2+b^2} = 2l$,which implies $a^2+b^2 = 4l^2$.Let $P(x, y)$ be the mid-point of the rod $AB$. Then $x = \frac{0+b}{2} = \frac{b}{2}$ and $y = \frac{a+0}{2} = \frac{a}{2}$.This gives $b = 2x$ and $a = 2y$.Substituting these values into the equation $a^2+b^2 = 4l^2$,we get $(2y)^2 + (2x)^2 = 4l^2$.$4x^2 + 4y^2 = 4l^2$,which simplifies to $x^2+y^2 = l^2$.Thus,the locus of the mid-point is $x^2+y^2 = l^2$.

$A$ rod of length $2l$ slides with its ends on two perpendicular lines. The locus of its mid-point is

Similar Questions

$A$ point on the straight line $3x + 5y = 15$ which is equidistant from the coordinate axes will lie only in

If the equation of the locus of a point equidistant from the points $(a_1, b_1)$ and $(a_2, b_2)$ is $(a_1 - a_2)x + (b_1 - b_2)y + c = 0$,then the value of $c$ is

$A$ moving line intersects the lines $x+y=0$ and $x-y=0$ at the points $A$ and $B$ respectively, such that the area of the triangle with vertices $(0,0)$, $A$, and $B$ has a constant area $C$. The locus of the mid-point of $AB$ is given by the equation:

The equation of the locus of a point which is equidistant from the points $(2, 3)$ and $(4, 5)$ is

If for a variable line $\frac{x}{a} + \frac{y}{b} = 1$,the condition $\frac{1}{a^2} + \frac{1}{b^2} = \frac{1}{c^2}$ ($c$ is a constant) is satisfied,then the locus of the foot of the perpendicular drawn from the origin to the line is:

Vedclass Test Series

Exam Paper Generator

Online Exam Module