There is a point (p,q) on the graph of `f(x)=x^2` and a point `(r , s)` on the graph of `g(x)=(-8)/x ,w h e r ep >0a n dr > 0.` If the line through `(p , q)a n d(r , s)` is also tangent to both the curves at these points, respectively, then the value of `P+r` is_________.

There is a point (p,q) on the graph of f(x)=x^(2) and a point (r,s) on the graph of g(x)=(-8)/(x), where p>0 and r>0. If the line through (p,q) and (r,s) is also tangent to both the curves at these points,respectively, then the value of P+r is

There is a point (p,q) on the graph of f(x)=x^(2) and a point (r,s) on the graph of g(x)=(-8)/(x),"where" g gt0 and rgt0. If the line through (p,q) and (r,s) is also tangent to both the curves at these points, respectively, then the value of (p+r) is "____"

A line lx+my+n=0 meets the circle x^(2)+y^(2)=a^(2) at points P and Q. If the tangents drawn at the points P and Q meet at R, then find the coordinates of R.

If p, q, r, s are in G.P, show that (p^n + q^n) , (q^n + r^n) , (r^n + s^n) are also in G.P

If a line through A(1, 0) meets the lines of the pair 2x^2 - xy = 0 at P and Q. If the point R is on the segment PQ such that AP, AR, AQ are in H.P then find the locus of the point R.

In Figure, P Q > P R. Q S\ a n d\ R S are the bisectors of /_ Q and /_R respectively. Prove that S Q > S R .

Tangent is drawn at any point (p ,q) on the parabola y^2=4a x .Tangents are drawn from any point on this tangant to the circle x^2+y^2=a^2 , such that the chords of contact pass through a fixed point (r , s) . Then p ,q ,r and s can hold the relation (A) r^2q=4p^2s (B) r q^2=4p s^2 (C) r q^2=-4p s^2 (D) r^2q=-4p^2s