The coordinates of the point on the curve $y=x^2+3 x+4$ the tangent at which passes through the origin is equal to

(2, 14), (–2, 2) (2, 14), (–2, –2) (2, 14), (2, 2) None of these

(2, 14), (–2, 2)

$\frac{d y}{d x}=2 x+3$ ∴ equation of tangent is Y - y = (2x + 3)(X - x) It passes through (0, 0),   ∴  -y = -x(2x + 3) $\Rightarrow y=x(2 x+3) \Rightarrow 2 x^2+3 x=x^2+3 x+4$ ⇒ x = 2, –2; y = 14, –2.