P is a variable point on the curve y= f(x) and A is a fixed point in the plane not lying on the curve. If `PA^(2)` is minimum, then the angle between PA and the tangent at P is

Let (a,b) and (lambda,u) be two points on the curve y=f(x). If the slope of the tangent to the curve at (x,y) be?

Let a curve P:(y-2)^2=x-1 If a tangent is drawn to the curve P at the point whose ordinate is 3 then the area between the tangent , curve and x-asis is

If ABCD is a square incribed in a circle and PA is a tangent, then the angle between the lines P'A and P'B is _________.

The minimum distance between a point on the curve y=e^(x) and a point on the curve y=log_(e)x is

The minimum distance between a point on the curve y=e^(x) and a point on the curve y=log_(e)x is -

A curve y=f(x) passes through the 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. Determine the equation of the curve. Also obtain the area bounded by the y-axis, the curve and the normal to the curve at P .

Let f (x) = [{:(1-x,,, 0 le x le 1),(0,,, 1 lt x le 2 and g (x) = int_(0)^(x) f (t)dt.),( (2-x)^(2),,, 2 lt x le 3):} Let the tangent to the curve y = g( x) at point P whose abscissa is 5/2 cuts x-axis in point Q. Let the pependiculat from point Q on x-axis meets the curve y =g (x) in point R. If 'theta' be the angle between tangents to the curve y =g (x) at point P and R, then tan theta equals to :

Consider f(x)=int_(1)^(x)(t+(1)/(t))dt and g(x)=f'(x) If P is a point on the curve y=f(x) such that the tangent to this curve at P is parallel to the chord joining the point ((1)/(2),g((1)/(2))) and (3,g(3)) of the curve then the coordinates of the point P