At the point `P(a,a^(n))` on the graph of `y=x^(n)(n in N)` in the first quadrant at normal is drawn. The normal intersects the Y-axis at the point (0, b). If `lim_(ararr0)b=(1)/(2)`, then n equals ……………

Find the point on the axis of the parabola 3y^2+4y-6x+8 =0 from when three distinct normals can be drawn.

The ordinates of points P and Q on the parabola y^2=12x are in the ration 1:2 . Find the locus of the point of intersection of the normals to the parabola at P and Q.

If f(x)=(a-x^(n))^(1/n) , where a gt 0 and n in N , then fof (x) is equal to

Find the equation of the line parallel to Y -axis and drawn through the point of intersection of the lines x-7y + 5=0 and 3x +y=0 .

Find the equations of the tangent and normal to the hyperbola (x^(2))/(a^(2))-(y^(2))/(b^(2))=1 at the point (x_(0), y_(0)) .

Three normals are drawn from the point (14,7) to the curve y^2-16x-8y=0 . Find the coordinates of the feet of the normals.

Three normals are drawn from the point (a,0) to the parabola y^2=x . One normal is the X-axis . If other two normals are perpendicular to each other , then the value of 4a is

For P(n):2^n = 0 ………..is true .

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

Find the equation of line parallel to the Y- axis and drawn through the point of intersection of x-7+5 = 0 and 3x + y -7=0 .