Q10 of 149 Page 16

At what point of the curve y = x2 does the tangent make an angle of 45o with the x–axis?

Given:


The curve is y = x2


Differentiating the above w.r.t x


⇒ y = x2


⇒ = 2x2 – 1


⇒ = 2x ...(1)


= The Slope of the tangent = tan


Since, the tangent make an angle of 45o with x – axis


i.e,


⇒ = tan(45°) = 1 ...(2)


tan(45°) = 1


From (1) & (2), we get,


⇒ 2x = 1


⇒ x =


Substituting x = in y = x2, we get,


⇒ y = ()2


⇒ y =


Thus, the required point is (,)


More from this chapter

All 149 →
8

Find a point on the curve y = x2 where the Slope of the tangent is equal to the x – coordinate of the point.

 9

At what point on the circle x2 + y2 – 2x – 4y + 1 = 0, the tangent is parallel to x – axis.

 11

Find a point on the curve y = 3x2 – 9x + 8 at which the tangents are equally inclined with the axes.

 12

At what points on the curve y = 2x2 – x + 1 is the tangent parallel to the line y = 3x + 4?