Find the points on the curve `x y+4=0` at which the tangents are inclined at an angle of `45o` with the x-axis.

Answer

Point`(x_{1}, y_{1})=(2,-2)`

Explanation

Let the required point be `(x_{1}, y_{1})`.

Slope of the tangent at point `=\tan 45^{\circ}`


ATQ:

`x y+4=0 . .(1)`

As point fulfills the above equation, then

`x_{1} y_{1}+4=0 . \ldots(2)`


On differentiating eq (2) both sides with respect to `x`, we get
$$
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