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+ris "____"`

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_________.

We are given the curves y=int_(-oo)^(x)f(t) dt through the point (0,(1)/(2)) and y=f(X), where f(x)gt0 and f(x) is differentiable, AAx in R through (0,1). If tangents drawn to both the curves at the point wiht equal abscissae intersect on the point on the X-axis, then int_(x to oo)(f(x))^f(-x) is

We are given the curves y=int_(-oo)^(x)f(t) dt through the point (0,(1)/(2)) and y=f(X), where f(x)gt0 and f(x) is differentiable, AAx in R through (0,1). If tangents drawn to both the curves at the point wiht equal abscissae intersect on the point on the X-axis, then The function f(x) is

If p^(th), q^(th) and r^(th) terms of G.P. are x,y,z respectively then write the value of x^(q-r) y^(r-p) z^(p-q).

A curve y=f(x) passes through point P(1,1) . The normal to the curve at P is a (y-1)+(x-1)=0 . If the slope of the tangent at any point on the curve is proportional to the ordinate of the point, then the equation of the curve is

Find the equation of line passing through the points P(-1,3,2) and Q(-4,2-2) . Also, if the point R(5,5,lambda) is collinear with the points P and Q, then find the value of lambda .

The chord joining the points where x = p and x = q on the curve y = ax^(2)+bx+c is parallel to the tangent at the point on the curve whose abscissa is

A tangent to the circle x^(2)+y^(2)=1 through the point (0, 5) cuts the circle x^(2)+y^(2)=4 at P and Q. If the tangents to the circle x^(2)+y^(2)=4 at P and Q meet at R, then the coordinates of R are

If the tangent at a point P with parameter t , on the curve x=4t^2+3 , y=8t^3-1 t in R meets the curve again at a point Q, then the coordinates of Q are

If the tangent at a point P with parameter t , on the curve x=4t^2+3 , y=8t^3-1 t in R meets the curve again at a point Q, then the coordinates of Q are