The tangent drawn at any point of the curve ` sqrtx+sqrty = sqrta` meets the OX and OY axes at points P and Q respectively, prove that OP+OQ = a.

The tangent at any point on the curve x=acos^3theta,y=asin^3theta meets the axes in Pa n dQ . Prove that the locus of the midpoint of P Q is a circle.

The tangent at any point on the curve x=acos^3theta,y=asin^3theta meets the axes in Pa n dQ . Prove that the locus of the midpoint of P Q is a circle.

The ordinate and the normal at any point P on the curve meet the x-axis at points A and B respectively. Find the equation of the family of curves satisfying the condition , The product of abscissa of P and AB =arithmetic mean of the square of abscissa and ordinate of P .

A tangent and a normal to a curve at any point P meet the x and y axes at A, B and C, D respectively. Find the equation of the curve passing through (1, 0) if the centre of circle through O.C, P and B lies on the line y = x (where O is the origin).

The area of the region bounded by the curve sqrtx+sqrty=sqrta(x,ygt0) and the coondinate axes is

Find the eqution of the curve passing through the point (1,1), if the tangent drawn at any point P(x,y) on the curve meets the coordinate axes at A and B such that P is the mid point of AB.

Tangent and normal at any point P of the parabola y^(2)=4ax(a gt 0) meet the x-axis at T and N respectively. If the lengths of sub-tangent and sub-normal at this point are equal, then the area of DeltaPTN is given by

Two circles touch externally at a point P . From a external point T on the tangent at P , tangents T Q and T R are drawn to the circles with points of contact Q and R respectively. Prove that T Q = T R .

If the tangent drawn to the hyperbola (x^2)/(a^2)-(y^2)/(b^2)=1 at any point P meets the coordinate axes at the points A and B respectively. If the rectangle OACB (O being the origin) is completed, where C lies on (x^2)/(a^2)-(y^2)/(b^2)=lambda . Then, the value of lambda is:

the tangent drawn at any point P to the parabola y^2= 4ax meets the directrix at the point K. Then the angle which KP subtends at the focus is