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
Answer & explanation
Correct answer: option 1
$\frac{d y}{d x}=2 x+3$
∴ 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.