Question

The point where normal to y=x²-2x+3 is parailel to Y-axis is ......,Select correct option from the given options.
(a) (0,3)
(b) (-1,2)
(c) (1,2)
(d) (3,6)

Answer 1

answer : option (c)

explanation : we have to find the point where normal to y = x² - 2x + 3 is parallel to Y-axis.

first differentiate equation of curve with respect to x,

i.e., dy/dx = 2x - 2

hence, slope of tangent ⇒dy/dx = 2x - 2

we know, normal to the curve is perpendicular on tangent to the curve.

so, slope of normal × slope of tangent = -1

or, slope of normal = -1/(2x - 2).....(1)

a/c to question,

normal is parallel to Y-axis.

slope of Y-axis = 1/0

so, slope of Y-axis = slope of normal

or, 1/0 = -1/(2x - 2)

or, 2x - 2 = 0

or, x = 1 putting in equation, y = x² - 2x + 3

so, y = (1)² - 2(1) + 3 = 2

hence, required point : (1,2)