
Find the point of intersection of normals at and on the parabola .
Answer
526.5k+ views
Hint: The given problem is related to the equation of normal to parabola in parametric form. The general equation of the normal to the parabola at a point is given by , where is a parameter.
Complete step-by-step answer:
We are given the equation of the parabola as .
Now, we will consider two points on the parabola given by and , where , and are parameters.
Now, we need to find the equation of normal at and .
We know, the general equation of the normal to the parabola at a point is given by , where is a parameter.
So, the normal to the parabola at the point will be given is given by substituting in place of in the general equation of the normal.
On substituting in place of in the general equation of the normal, we get .
And the normal to the parabola at the point is given as .
Now, to find the point of intersection of and , we substitute the value of from equation in equation .
On substituting the value of from equation in equation , we get .
Now, we will substitute in equation .
On substituting in equation , we get .
So, the point of intersection of the normal is .
Note: While simplifying the equations, please make sure that sign mistakes do not occur. These mistakes are very common and can confuse while solving. Ultimately the answer becomes wrong. So, sign conventions should be carefully taken.
Complete step-by-step answer:
We are given the equation of the parabola as
Now, we will consider two points on the parabola given by

Now, we need to find the equation of normal at
We know, the general equation of the normal to the parabola at a point
So, the normal to the parabola at the point
On substituting
And the normal to the parabola at the point
Now, to find the point of intersection of
On substituting the value of
Now, we will substitute
On substituting
So, the point of intersection of the normal is
Note: While simplifying the equations, please make sure that sign mistakes do not occur. These mistakes are very common and can confuse while solving. Ultimately the answer becomes wrong. So, sign conventions should be carefully taken.
Recently Updated Pages
Master Class 11 Economics: Engaging Questions & Answers for Success

Master Class 11 Accountancy: Engaging Questions & Answers for Success

Master Class 11 English: Engaging Questions & Answers for Success

Master Class 11 Social Science: Engaging Questions & Answers for Success

Master Class 11 Physics: Engaging Questions & Answers for Success

Master Class 11 Biology: Engaging Questions & Answers for Success

Trending doubts
How many moles and how many grams of NaCl are present class 11 chemistry CBSE

How do I get the molar mass of urea class 11 chemistry CBSE

Define least count of vernier callipers How do you class 11 physics CBSE

Plants which grow in shade are called A Sciophytes class 11 biology CBSE

A renewable exhaustible natural resource is A Petroleum class 11 biology CBSE

In which of the following gametophytes is not independent class 11 biology CBSE
