Locus

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

The equation of the locus of the points equidistant from the points $A\left(-2,3\right)$ and $B\left(6,-5\right)$ is

A line segment of fixed length $2$ units moves so that its ends are on the positive $x-$axis and on the part of the line $x+y=0$ which lies in the second quadrant. Then, the locus of the mid-point of the line has the equation 

A point $P$ moves so that the sum of squares of its distances from the points $\left(1,2\right)$ and $\left(-2,1\right)$ is $14$. Let $f\left(x,y\right)=0$ be the locus of $P$ which intersects the $x$-axis at the points $A$ and $B$ and the $y-$axis at the points $C$ and $D$. Then the area of the quadrilateral $ABCD$ is equal to

Find the locus of centroid of triangle $ABC$ with $A\left(\cos \theta ,0\right)$, $B\left(0,\sin \theta \right)$ and $C\left(0,0\right)$ and $\theta \in \left(0,90°\right)$.

The locus of mid-points of the perpendiculars drawn from points on the line $x=2y$ to the line $x=y$ is

The locus of the mid-point of the portion of a line of constant slope '$m$' between two branches of the rectangular hyperbola $xy=1$ is

The Locus of the point $\left(\tan \theta +\sin \theta , \tan \theta -\sin \theta \right)$ is ($\theta$ isa parameter)

$A\left(0,4\right),B\left(0,-4\right)$ are two points. The locus of $P$ which moves such that $\left|PA-PB\right|=6$ 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

If $P$ lies on the line $y=x$ and $Q$ lies on $y=2x$ and $\left|PQ\right|=4$ then the mid point of $PQ$ lies on the curve

A variable line through $A\left(6,8\right)$ meets the curve $x^2+y^2=2$ at $B$ and $C$. $P$ is a point on $BC$ such that $AB,AP,AC$ are in $\mathrm{HP}$. The minimum distance of the origin from the locus of $P$ is

A line segment of length $2l$ sliding with ends on the axes, then the locus of the middle point of the line segment is 

$p,x_1,x_2,\dots ,x_n$ and $q,y_1,y_2,\dots ,y_n$ are two arithmetic progressions with common differences $a$ and $b$ respectively. If $\alpha$ and $\beta$ are the arithmetic means of $x_1,x_2,\cdots ,x_n$ and $y_1,y_2,\cdots ,y_n$ respectively, then the locus of $P\left(\alpha ,\beta \right)$ 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 $\left(4,3\right)$.