Coordinate Geometry Set-2

Q1. Find the midpoint of the line segment joining the points $(2,-3)$ and $(8,5)$.

Q2. The perpendicular bisector of the segment joining $(2,3)$ and $(6,-1)$ has equation:

Q3. Let $A(2,1)$ and $B(6,5)$. The circle whose centre is the midpoint of $AB$ and which passes through $A$ has equation:

Q4. Point $P$ lies on the $x$-axis. If $A(2,3)$ and $B(8,5)$, for which point(s) $P$ does the area of $\triangle ABP$ equal $6$?

Q5. Find the centres of all circles which pass through the points $(1,4)$ and $(5,2)$ and are tangent to the $x$-axis.

Q6. The midpoint of the line segment joining the points $A(2,-3)$ and $B(-4,5)$ is

Q7. A point $P$ lies on the $x$-axis and is equidistant from $A(3,4)$ and $B(7,2)$. The coordinates of $P$ are

Q8. The vertices of triangle $ABC$ are $A(2,3)$, $B(5,-1)$ and $C(x,2)$. If the area of $\triangle ABC$ is $7$ square units, the possible values of $x$ are

Q9. Let $P(x,y)$ be a point such that its distance from the origin is twice its distance from $(4,0)$. The locus of $P$ is the circle

Q10. A circle passes through the points $(1,0)$ and $(-1,0)$ and its center lies on the line $x+2y=3$. The equation of this circle is

Q11. Find the midpoint of the line segment joining $A(2,-3)$ and $B(8,5)$.

Q12. The perpendicular bisector of the segment joining $P(1,2)$ and $Q(5,-2)$ is which of the following lines?

Q13. Point $R$ divides the line segment joining $A(1,4)$ and $B(6,-1)$ internally in the ratio $AP:PB=2:3$. Coordinates of $R$ are

Q14. The vertices of a triangle are $A(1,2),\;B(5,6),\;C(9,2)$. The equation of its circumcircle is

Q15. Point $P$ divides the line segment joining $A(2,1)$ and $B(8,5)$ externally in the ratio $AP:PB=2:3$. The coordinates of $P$ are