If `P=(1,1),Q=(3,2)` and `R` is a point on x-axis then the value of `PR+RQ` will be minimum at

Given points P(2,3),Q(4,-2), and R(alpha,0). Find the value of a if PR+RQ is minimum.

If P,Q and R are three points with coordinates (1,4),(4,5) and (m,m) respectively,then the value of m for which PR+RQ is minimum,is:

If P-=(-2, -3) and Q-= (3, 7) , then point A on the X- axis such that AP^(2)+AQ^(2) is minimum is

Given three points P,Q,R with P(5,3) and R lies on the x-axis. If equation of RQ is x-2y=2 and PQ is parallel to the x-axis, then the centroid of DeltaPQR lies on the line:

Let P be (5,3) and a point R on y = x and Q on the X - axis be such that PQ +QR+RP is minimum ,then the coordinates of Q are

If P(-2,2,3) and Q(13,-3,13) are two points. Find the locus of point R which moves such that 3PR=2QR

A man strats from the point P(-3,4) and reaches the point Q(0,1) touching the x-axis at R(alpha,0) such that PR+RQ is minimum. Then |alpha|= .

A man starts walking from the point P( -3, 4), touches the x-axis at R, and then turns to reach at the point Q(0, 2). The man is walking at a constant speed. If the man reaches the point Q in the minimum time, then 50 ((PR)^2 + (RQ)^2) is equal to __________ .

A man starts walking from the point P( -3, 4), touches the x-axis at R, and then turns to reach at the point Q(0, 2). The man is walking at a constant speed. If the man reaches the point Q in the minimum time, then 50 ((PR)^2 + (RQ)^2) is equal to __________ .