Question

If normal to the curve y fx) at a point makes 135 angle with x- axis (taken counter-clocks positive x-axis) then at that point dy dx equals.

Answer 1

Answer:1

Step-by-step explanation:

1.) dy/dx = slope of the tangent to the curve y=f(x) at a point .

2.) Since relation between the slopes of the two perpendicular lines is

m1 × m2 = -1 ; where m1 , m2 are the slopes of two perp. lines .

3.) And Normal to the curve at the same point is also perpendicular to the tangent of the curve so by (1.) and

(2.) steps the slope of normal would be

-(dx/dy) == slope of normal .

4.) since normal is also making an angle of 135° with x-axis in counter clock wise direction so the slope of the normal is tan(135°)= -1

5.) On equating the values of slope from step (3.) and (4.) we get

-(dx/dy)= -1

and hence dy/dx = 1 .