Equation of Locus

Locus of the foot of the perpendicular drawn from a fixed point $(10, 0)$ on the $\mathrm{X}$-axis to any tangent to the circle $x^2+y^2=16$ is

Let $A\left(5,-3\right), B\left(3,-2\right), C\left(-1,5\right)$ be three points. If $P$ is a point satisfying the condition $P{A}^2+2P{B}^2=3P{C}^2$, then a point that lies on the locus of $P$ is

From a point $A\left(0,3\right)$ on the circle ${\left(x+2\right)}^2+{\left(y-3\right)}^2=4$, a chord $AB$ is drawn and it is extended to a point $Q$ such that $AQ=2 AB$. Then the locus of $Q$ is

If the perimeter of a triangle is $20$ and two of its vertices are $\left(-5,0\right)$ and $\left(6,0\right)$, then the locus of the third vertex is
tions:

Suppose $P$ and $Q$ are the mid points of the sides $AB$ and $BC$ of a triangle where $A\left(1,3\right), B\left(3,7\right)$ and $C\left(7,15\right)$ are vertices. Then the locus of $R$ satisfying $A{C}^2+Q{R}^2=P{R}^2$ is

A stick of length $r$ units slides with its ends on coordinate axes. Then the locus of the midpoint of the stick is a curve whose length is

Find the locus of the point which is at $9$ units distance from the point $\left(3,5\right)$

Write the equation to represent the locus of the points that is equidistant from the points $(3,2)$ and $\left(4,3\right)$.

Find the locus of the point moving on a plane which is at a fixed distance $5$ units from a the X axis.

Find the locus of a point which is at a fixed distance $4$ units from the origin.

A straight rod of length $4$ units slides such that its ends ${}^{\text{'}}A^{\text{'}}$ and ${}^{\text{'}}B^{\text{'}}$ always lie on the $x$ and $y$ axes, respectively. Then the locus of the centroid of $∆OAB$ is

The sum of the squares of the distances of a moving point from $2$ fixed points $A(a, 0)$ and $B(-a, 0)$ is equal to a constant $2{\mathrm{c}}^2,$ then the equation of its locus is

Find the locus of the point $\left(x, y\right)$ given by $x=2 \cos t+3$ and $y=2 \sin t+5$ where $t$ is a parameter.

Find the locus of the middle point of the portion of the line segment made by the straight line $x \mathrm{co}s\alpha +y \sin \alpha =4$  and the axes of co-ordinates.

A point moves in such a way that its distances from the points $A\left(3, \frac{\pi }{4}\right)$ and $B\left(5, \frac{3\pi }{4}\right)$ are always eqaul.

A point moves so that the sum of its distances from $\left(ae, 0\right)$ and $\left(-ae, 0\right)$ is $2 a$. Prove that the equation of its locus is $\frac{x^2}{a^2}+\frac{y^2}{b^2}=1$, where $b^2=a^2\left(1-e^2\right)$

If $O$ is the origin and $Q$ is a variable point on $y^2=x$, show that the locus of the mid-point of $OQ$ is $2y^2=x$

If $O$ is the origin and $Q$ is a variable point on $y^2=x$, show that the locus of the mid-point of $OQ$ is $2y^2=x$

A rod of length $P$ slides between two perpendicular lines. Find the locus of the point on the rod which divides it is the ratio $1:2$.

The co-ordinates of a variable point $P$ are $\left(a{t}^2, 2at\right)$, where $t$ is a parameter. A point $Q$ divides $OP$ internally in the ratio $m:n$($O$ is the origin). Find the equation of the locus of $Q$