Question

The number of normals drawn to the parabola \( y^{2} = 4x \) from the point \( (1, 0) \) is

• A. 0
• B. 1
• C. 2
• D. 3

Hint:

From a point $(h, 0)$ on the axis, three distinct normals exist only if $h>2a$.

Answer 1

The Correct Option is B

Step 1: Point Analysis
The given point $(1, 0)$ is the focus of the parabola $y^{2}=4x$.
Step 2: Graphical Analysis
For any point on the axis of the parabola $(x, 0)$, if $x \le 2a$, only one normal can be drawn (the axis itself). Here $a=1$, so $2a=2$. Since $1<2$, only the axis $y=0$ is a normal.
Final Answer: (b)