Find all possible values of x for which the distance between the points A(x,−1) and B(5,3) is 5 units.
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The line joining the points A(2,1),andB(3,2)
is perpendicular to the line (a2)x+(a+2)y+2=0.
Find the values of a˙
Find the locus of the point of intersection of lines xcosα+ysinα=a
is a variable).
A point moves such that the area of the triangle formed by it with the points (1, 5) and (3,−7)is21squ˙nits˙ Then, find the locus of the point.
If the circumcenter of an acute-angled triangle lies at the origin and the centroid is the middle point of the line joining the points (a2+1,a2+1)
then find the orthocentre.
In each of the following find the value of k, for which the points are collinear.(i) (7,−2),(5,1),(3,k)(ii) (8,1),(k,−4),(2,−5)
Consider three points P=(−sin(β−α),−cosβ), Q=(cos(β−α),sinβ), and R=((cos(β−α+θ),sin(β−θ)), where 0<α,β,θ<4π Then
Prove that the circumcenter, orthocentre, incenter, and centroid of the triangle formed by the points A(−1,11),B(−9,−8),
are collinear, without actually finding any of them.