Maths-

General

Easy

Question

# Three normals are drawn to the parabola from the point (c, 0) These normals are real and distinct when

- c=0
- c=1
- c=2
- c=3

Hint:

### A normal in geometry is a piece of geometry that is perpendicular to another piece of geometry, such as a line, ray, or vector. For instance, the (infinite) line perpendicular to the tangent line to the curve at the point is the normal line to a plane curve at the point. Here we have to find these normals are real and distinct at what c.

## The correct answer is: c=3

### At a specific point on a curve, tangents and normals behave just like any other straight lines. The normal runs perpendicular to the curve, and a tangent is parallel to the curve at the point. Like any other straight line, the equation of tangent and normal can be evaluated.

Here we have given parabola of y^{2} = 4x.

So here we used the concept of tangents and normals, we found the slope and then went to proceed with the final answer. The normal to a parabola is perpendicular to the tangent of the parabola. So here the value of c is 3.

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