yes i want to know why we have to calculate the coordinates with the gradient of the tangent and not with the gradient of the normal in this particular question, as i've solved this problem, but after converting the gradient 1 to -1, please tell me that
and thanks for the reply and procedure
No you did not read it very closely.
The normal is perpendicular to the tangent not to the given line.
So that case you are finding where the tangent to the curve is perpendicular to the given line.
Recall from basic geometry, two lines perpendicular to the same line, in this case the tangent, are themselves parallel.