2
$\begingroup$

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...

$\endgroup$
1
  • 2
    $\begingroup$ Possible duplicate of A question on parabola $\endgroup$ – user147263 Oct 20 '15 at 13:16
1
$\begingroup$

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,

$\endgroup$
0
0
$\begingroup$

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

$\endgroup$

Your Answer

By clicking “Post Your Answer”, you agree to our terms of service, privacy policy and cookie policy

Not the answer you're looking for? Browse other questions tagged or ask your own question.