2

Consider the following lines

  1. $x-y-1=0$
  2. $x+y-5=0$
  3. $y=4$

The line 1 is the axis of the parabola, the line 2 is the tangent at the vertex to the same parabola, and the line 3 is another tangent to the same parabola at some point $P$.

Now let a circle $C$ circumscribing the triangle formed by tangent and normal at the point $P$ and the axis of the parabola.

Then how can I find the equation of the circle?

I have tried and found that the vertex of this parabola is (3,2). Need help....don't know how to proceed further.... Thanks in advance...

gt6989b
  • 54,422
Aditya
  • 598

2 Answers2

1

The problem does NOT ask you to find the equation of the parabola nor does this problem really have anything to do with a parabola, strictly speaking. The problem asks you to find the circle passing through the three points of intersection of the lines y= x+ 1, y= 5- x, and y= 4.

What are those three points? How do you find the equation of a circle passing through those points,

user247327
  • 18,710
0

If equation of axis, tangent at vertex and another tangent is given then it is possible to work out the equation by finding focus and directrix. I have solved a similar question in one of my videos. Pls have a look https://youtu.be/U9MTLxq8qFM

Mathsmerizing
  • 2,003