The equation of the line passing through (–4, 3, 1), parallel

to the plane x + 2y – z – 5 = 0 and intersecting

the line $${{x + 1} \over { - 3}} = {{y - 3} \over 2} = {{z - 2} \over { - 1}}$$ is :

Equation of a common tangent to the circle, x² + y² – 6x = 0 and the parabola, y² = 4x is :

The plane through the intersection of the planes x + y + z = 1 and 2x + 3y – z + 4 = 0 and parallel to y-axis also passes through the point :

If $$\theta $$ denotes the acute angle between the curves, y = 10 – x² and y = 2 + x² at a point of their intersection, the |tan $$\theta $$| is equal to :