Find a pair of curves such that (a) the tangents drawn at points with equal abscissas intersect on the y-axis. (b) the normal drawn at points with equal abscissas intersect on the x-axis. (c) one curve passes through (1,1) and other passes through (2, 3).

A pair of curves y=f_1(x) and y=f_2(x) are such that following conditions are satisfied.(i) The tangents drawn at points with equal abscissae intersect on y-axis.(ii) The normals drawn at points with equal abscissae intersect on x-axis. Answer the question:Which of the following is true (A) f\'_1(x)+f\'_2(x)=c (B) f\'_1(x)-f\'_2(x)=c (C) f\'_1^2(x)-f\'_1^2(x)=c (D) f\'_1^2(x)+f\'_2^2(x)=c

A curve is such that the mid-point of the portion of the tangent intercepted between the point where the tangent is drawn and the point where the tangent is drawn and the on the line y=x. If the curve passes through (1,0), then the curve is

The tangent to the curve y=xe^(x^2) passing through the point (1,e) also passes through the point

A tangent and a normal to a curve at the point (x,y) make equal intercepts on the x -axis and they-axis respectively.Find the curve which passes through the point (1,1)

Find the equation of the curve which is such that the area of the rectangle constructed on the abscissa of any point and the intercept of the tangent at this point on the y-axis is equal to 4.

A curve is such that the ratio of the subnomal at any point to the sum of its co-ordinates is equal tothe ratio of the ordinate of this point to its abscissa.If the curve passes through M(1,0), then possible equation of the curve is(are)

Given the curves y=f(x) passing through the point (0,1) and y=int_(-oo)^(x) f(t) passing through the point (0,(1)/(2)) The tangents drawn to both the curves at the points with equal abscissae intersect on the x-axis. Then the curve y=f(x), is

The curve such that the intercept on the X-axis cut-off between the origin, and the tangent at a point is twice the abscissa and passes through the point (2, 3) is