Two points P(a,0) and Q(-a,0) are given. `R` is a variable point on one side of the line `P Q` such that `/_R P Q-/_R Q P` is a positive constant `2alphadot` Find the locus of the point `Rdot`

A point R with x-coordinate 4 lies on the line segment joining the points P(2,-3,4) and Q(8,0,10) . Find the coordinates of the point R.

Given that P(3,1),Q(6. 5), and R(x , y) are three points such that the angle P Q R is a right angle and the area of R Q P is 7, find the number of such points Rdot

Let O(0,0),P(3,4), and Q(6,0) be the vertices of triangle O P Q . The point R inside the triangle O P Q is such that the triangles O P R ,P Q R ,O Q R are of equal area. The coordinates of R are (a) (4/3,3) (b) (3,2/3) (c) (3,4/3) (d) (4/3,2/3)

If the points P(6,2) and Q(-2,1) and R are the vertices of a DeltaPQR and R is the point on the locus of y=x^(2)-3x+4 , then find the equation of the locus of centroid of DeltaPQR .

If a point Q lies between two points P and R such that PQ = QR, prove that PQ = 1/2 PR.

Let P be a point on the ellipse x^2/a^2+y^2/b^2=1 , 0 < b < a and let the line parallel to y-axis passing through P meet the circle x^2 +y^2=a^2 at the point Q such that P and Q are on the same side of x-axis. For two positive real numbers r and s, find the locus of the point R on PQ such that PR : RQ = r : s and P varies over the ellipse.