Would the following working help with question 18?
Integrating, we get:
In order to find the value of this constant, we need to understand that the gradient of the tangent at (-1,3) is perpendicular to the gradient of the line
Rearranging results in:
Therefore, the gradient of the tangent is 2, as the product of perpendicular gradients is -1.
Substituting this into
![1644544084522.png](/data/attachments/34/34932-38bc8f48b0f0162ac970cb2044c50896.jpg)
:
Integrating again, we get:
![1644544201958.png](/data/attachments/34/34934-38c23913a64536258cc40aa8531f6f1e.jpg)
The point (-1,3) is on this curve. Using this information in the equation:
Hence, the equation of the curve is:
![1644544320621.png](/data/attachments/34/34936-6384c9ca301234189fc29fba33790e08.jpg)