Q4 of 168 Page 242

Find the equation of the normal to curve x2 = 4y which passes through the point (1, 2).

It is given that curve is y2 = 4x.

Differentiating with respect to x, we get,





Now, the slope of the normal at point (1,2) is


Therefore, Equation of the normal at (1,2) is y - 2 = - 1(x – 1)


⇒ y - 2 = - x + 1


⇒ x + y - 3 = 0


More from this chapter

All 168 →
2

Show that the function given by has maximum at x = e.

 3

The two equal sides of an isosceles triangle with fixed base b are decreasing at the rate of 3 cm per second. How fast is the area decreasing when the two equal sides are equal to the base?

 5

Show that the normal at any point θ to the curve

x = a cosθ + a θ sinθ, y = a sinθ – aθ cosθ is at a constant distance from the origin.

 6

Find the intervals in which the function f given by


is (i) strictly increasing (ii) strictly decreasing.