Find the point on the curve at which the tangent passes through the origin.
If tangent is pass through origin it means that equation of tangent is y = mx
Let us suppose that tangent is made at point (x1, y1)
y1 = x12 + 3x1 + 4 …(1)
m at (x1, y1) = 2x1 + 3
Equation of tangent : y1 = (2x1 + 3)x1 …(2)
On compairing eq(1) and eq(2)
x12 + 3x1 + 4 = (2x1 + 3)x1
x12 – 4 = 0 ⇒ x1 = 2 and -2
At x1 = 2, y1 = 14
At x1 = -2, y1 = 2
So, required points are (2, 14) and (-2, 2)