The tangent to the circle C₁ : x² + y² $$-$$ 2x $$-$$ 1 = 0 at the point (2, 1) cuts off a chord of length 4 from a circle C₂ whose center is (3, $$-$$2). The radius of C₂ is :

Tangents drawn from the point ($$-$$8, 0) to the parabola y² = 8x touch the parabola at $$P$$ and $$Q.$$ If F is the focus of the parabola, then the area of the triangle PFQ (in sq. units) is equal to :

An angle between the lines whose direction cosines are gien by the equations,
$$l$$ + 3m + 5n = 0 and 5$$l$$m $$-$$ 2mn + 6n$$l$$ = 0, is :

A normal to the hyperbola, 4x² $$-$$ 9y² = 36 meets the co-ordinate axes $$x$$ and y at A and B, respectively. If the parallelogram OABP (O being the origin) is formed, then the ocus of P is :