Let P(h, k) be a point on the curve
y = x² + 7x + 2, nearest to the line, y = 3x – 3.
Then the equation of the normal to the curve at P is :

The plane passing through the points (1, 2, 1),
(2, 1, 2) and parallel to the line, 2x = 3y, z = 1
also passes through the point :

If the tangent to the curve y = x + sin y at a point
(a, b) is parallel to the line joining $$\left( {0,{3 \over 2}} \right)$$ and $$\left( {{1 \over 2},2} \right)$$, then :

If R = {(x, y) : x, y $$ \in $$ Z, x² + 3y² $$ \le $$ 8} is a relation on the set of integers Z, then the domain of R^–1 is :