A tangent is drawn to the parabola `y^2=4 x` at the point `P` whose abscissa lies in the interval (1, 4). The maximum possible area of the triangle formed by the tangent at `P ,` the ordinates of the point `P ,` and the x-axis is equal to

If focal distance of a point P on the parabola y^(2)=4ax whose abscissa is 5 10, then find the value of a.

Tangents are drawn to the parabola y^2=4a x at the point where the line l x+m y+n=0 meets this parabola. Find the point of intersection of these tangents.

The area of the figure bounded by the parabola (y-2)^(2)=x-1, the tangent to it at the point with the ordinate y=3, and the x-axis is

The area (in sq. units) bounded by the parabola y=x^2-1 , the tangent at the point (2,3) to it and the y-axis is

The tangent to the parabola y=x^2 has been drawn so that the abscissa x_0 of the point of tangency belongs to the interval [1,2]. Find x_0 for which the triangle bounded by the tangent, the axis of ordinates, and the straight line y=x0 2 has the greatest area.

Tangents are drawn to the hyperbola 4x^2-y^2=36 at the points P and Q. If these tangents intersect at the point T(0,3) then the area (in sq units) of triangle PTQ is

Find the area of the triangle formed by the tangents from the point (4, 3) to the circle x^2+y^2=9 and the line joining their points of contact.

Find by integration the area of the triangle formed by the x-axis and the tangent and normal to the parabola y=6x-x^(2) at (5,5)

The area of the triangle formed by the positive x-axis, and the normal and tangent to the circle x^2+y^2=4 at (1,sqrt3) is

The mirror image of the parabola y^2= 4x in the tangent to the parabola at the point (1, 2) is: