Let P be a point on the circle `x^(2) + y^(2) = a^(2)` whose ordinate is PN and Q is a point on PN such that PN : QN = 2 : 1 . Find the locus of Q and identify it

Let P b any point on the hyperbola (x^(2))/(a^(2))-(y^(2))/(b^(2))=1 whose ordinate is PN. AA′ is its transverse axis. If the point Q divides AP in the ratio a^(2):b^(2) , then NQ is?

Q is any point on the circle x^(2) +y^(2) = 9. QN is perpendicular from Q to the x-axis. Locus of the point of trisection of QN is

Q is any point on the circle x^(2) +y^(2) = 9. QN is perpendicular from Q to the x-axis. Locus of the point of trisection of QN is

PN is any ordinate of the parabola y^(2) = 4ax , the point M divides PN in the ratio m: n . Find the locus of M .

Q is any point on the parabola y^(2) =4ax ,QN is the ordinate of Q and P is the mid-point of QN ,. Prove that the locus of p is a parabola whose latus rectum is one -fourth that of the given parabola.