The tangent to the parabola y² = 4x at the point where it intersects the circle x² + y² = 5 in the first quadrant, passes through the point :

The shortest distance between the line y = x and the curve y² = x – 2 is :

The equation of a tangent to the parabola, x² = 8y, which makes an angle $$\theta $$ with the positive directions of x-axis, is :

The maximum area (in sq. units) of a rectangle having its base on the x-axis and its other two vertices on the parabola, y = 12 – x² such that the rectangle lies inside the parabola, is :