Tag: division of a line segment

If $(2, 3), (-4, 5), (1, -2)$ are the midpoints of the sides $\vec{BC}, \vec{CA}, \vec{AB}$ of $\triangle ABC$, then the equation of $\vec{AB}$ is 

The point on $X-axis$ equidistant from $(2,3)$and $(1,5)$ is

Let ${P} _{1}$ and ${P} _{2}$ be two fixed points in $xy-plane$. A line ${L} _{1}=0$ passes through ${P} _{1}$ intersects $y-axis$ at $B$ and the line ${L} _{2}=0$ passes through ${P} _{2}$ and intersects $x-axis$ at $A$. If ${L} _{1}=0$ and ${L} _{2}=0$ are perpendicular then the locus of mid-point of$AB$ is

The point which is equidistant from the points $(-1,1,3),(2,1,2),(0,5,6)$ and $(3,2,2)$ is

The point (5,0) on y-axis is equidistant from (-1,2) and (3,4).

The co-ordinates of the mid point joining the points $(sin^2 \theta, sec^2 \theta )$ and $(cos^2 \theta - tan^2 \theta)$ is

The point on $X$-axis which is equidistant from the point $\left( 3,5 \right )$ and $\left( 4,2 \right )$ is 

Let P be the point (1, 0) and Q a point on the curve ${ y }^{ 2 }=8x$. The locus of mid point of PQ is-

The co -ordinates of the midpoint of a line segment joining $ p(5,7) $ and $ Q (-3,3) $ are........

If Q is a variable point on $x^2=4y$ and O is the origin, the locus of mid point OQ is equation of