Pair of tangents are drawn from  P(−1, 2)  to  y2  =  4x  touching it at  A, B , then area of triangle  PAB  (in sq. units) is equal to:

The given equation represents a parabola with the vertex at the origin (0,0) and the focus at (1,0). The directrix of the parabola is the line x = -1.

The point P(-1,2) lies on the directrix of the parabola. Therefore, the tangents from P to the parabola are perpendicular to the directrix. These tangents intersect the parabola at points A and B.

The coordinates of A and B can be found by solving the equations of the tangents and the parabola. However, since the tangents are perpendicular to the directrix, the x-coordinates of A and B are the same and equal to 1 (the x-coordinate of the focus).

Therefore, the coordinates of A and B are (1,y1) and (1,y2), where y1 and y2 are the y-coordinates of the points where the tangents intersect the parabola.

Substituting x = 1 in the equation of the parabola, we get y^2 = 4*1 = 4. Therefore, y1 = 2 and y2 = -2.

So, the coordinates of A and B are (1,2) and (1,-2) respectively.

The area of triangle PAB is given by the formula 1/2 * base * height.

Here, the base of the triangle is the line segment AB, which has length 4 units (from -2 to 2 on the y-axis). The height of the triangle is the distance from P to the line AB, which is 2 units (from -1 to 1 on the x-axis).

Therefore, the area of triangle PAB is 1/2 * 4 * 2 = 4 square units.