Question

The normal to a curve at P(x, y) meets the x-axis at G. If the distance of G from the origin is twice the abscissa of P, then the curve is a 

(A)  circle

(B)   hyperbola 

(C)  ellipse 

(D)  parabola

Answer 1

Correct option  (b),(c)

Explanation :

The normal at P(x₁, y₁) is

y - y₁ = -1/m(x - x₁)

where

m(dy/dx)_(x1,y1)

Now, y = 0 ⇒ x₁ + my₁ + my₁ so that by hypothesis, we have

|x₁ + my₁| = 2|x₁|

Therefore, x₁ +  my₁ = ±2x₁.

which is a hyperbola.

which is an ellipse.