Answer :

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)


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