The tangent at a point `P` of a curve meets the axis of `y` in `N`, the line through `P` parallel to the axis of `y` meets the axis of `x` at `M`, `O` is the origin. If the area of `/_\MON` is constant. Show that the curve is a hyperbola.

The tangent at a point 'P' of a curve meets the axis of 'y' in N, the parallel through 'P' to the axis of 'y' meets the axis of X at M, O is the origin of the area of Delta MON is constant then the curve is (A) circle C) ellipse (D) hyperbola (B) parabola

The tangent at a point P of a curve meets the y-axis at A, and the line parallel to y-axis at A, and the line parallel to y-axis through P meets the x-axis at B. If area of DeltaOAB is constant (O being the origin), Then the curve is

If the tangent at any point P of a curve meets the axis of XinTdot find the curve for which O P=P T ,O being the origin.

The tangent at any point P on y^2 = 4x meets x-axis at Q, then locus of mid point of PQ will be

The tangent to the curve y = e^(2x) at (0,1) meets the x-axis at

Find the points on the curve y=4x^3-3x+5 at which the equation of the tangent is parallel to the X-axis.

The normal PG to a curve meets the x-axis in G. If the distance of G from the origin is twice the abscissa of P, prove that the curve is a rectangular hyperbola.

The point on the curve y=x^(3) at which the tangent to the curve is parallel to the X-axis, is

The tangent at any point P of a curve C meets the x-axis at Q whose abscissa is positive and OP = OQ, O being the origin, the equation of curve C satisfying these conditions may be

Let the tangent at a point P on the ellipse meet the major axis at B and the ordinate from it meet the major axis at A. If Q is a point on the AP such that AQ=AB , prove that the locus of Q is a hyperbola. Find the asymptotes of this hyperbola.