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 "____"`

The chord of the curve ax^(2)+bx+c=0 , joining the points x=p and x=q on the curve is parallel to the tangent to the curve at x=c where -

let P be the point (1, 0) and Q be a point on the locus y^2= 8x . The locus of the midpoint of PQ is

Let P be the point (1,0) and Q be a point on the locus y^(2)=8x . The locus of the midpoint of PQ is

If the pth , qth and rth terms of an A.P. be P, Q and R respectively then show that, p(Q-R) + q(R-P) + r(P-Q) = 0 .

P and Q are two points ona circle with centre at O. R is a point on the minor arc of the circle, between the points P and Q. The tangents to the circle at the points P and Q meet each other at the points S. If anglePSQ =20^@ , then anglePRQ =

If the tangent at any point P(4m^(2),8m^(3)) of x^(3)-y^(2)=0 normal also to the curve x^(3)-y^(2)=0 , then the value of m is-

If the p^(th) , q^(th) and r^(th) terms of a G.P. are x , y , z respectively. then show that : x^(q-r) . y^(r-p).z^(p-q)=1

If the equation x^2+px+qr=0 and x^2+qx+pr=0(p!=q,r!=0) has same root then prove that p+q+r=0

Let f'(x)gt0 and g'(x)lt0 for all x in R, then

Let , RS be the diameter of the circle x^(2) + y^(2) = 1 , where S is the point ( 1,0) . Let P be a variable point (other then R and S ) on the circle and tangents to the circle at s and P meet at the point Q . The normal to the circle at P intersects a line drawn through Q parallel to RS at point E . The locus of E passes through the point (s)