Find the coordinates of the points on the curve `y=x^2+3x+4,` the tangents at which pass through the origin.

Answer

Points are `(2,14) and (-2,2)`

Explanation

When line passes through origin `y=m x`, then slope of tangent of a curve becomes `\frac{d y}{d x}` at that point.


`\therefore y=x^2+3 x+4`

`\Rightarrow \frac{dy}{dx}=2 x+3`


Pt. `(x, y)`

`y_1=mx_1 \rightarrow` (i)

`y_2=x_1^2+3 x_1+4 \rightarrow` (ii)

`m=2 x_1+3`

Putting value in (i)

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