Find The Locus Of The Poles Of The Normal Of The Hyperbola .

Why Kaysons ?

Video lectures

Access over 500+ hours of video lectures 24*7, covering complete syllabus for JEE preparation.

Online Support

Practice over 30000+ questions starting from basic level to JEE advance level.

Live Doubt Clearing Session

Ask your doubts live everyday Join our live doubt clearing session conducted by our experts.

National Mock Tests

Give tests to analyze your progress and evaluate where you stand in terms of your JEE preparation.

Organized Learning

Proper planning to complete syllabus is the key to get a decent rank in JEE.

Test Series/Daily assignments

Give tests to analyze your progress and evaluate where you stand in terms of your JEE preparation.

SPEAK TO COUNSELLOR ? CLICK HERE

Question

Find the locus of the poles of the normal of the hyperbola .

Solution

Correct option is

(a2 + b2)2

Let (x1, y1) be the pole of the normal chord.

Equation of polar is .

But polar is a normal chord.

⇒ its equation is

                …. (2)

On comparing (1) and (2),

        

And 

Using  ,

we get

        

 

Testing

SIMILAR QUESTIONS

Q1

The equation of normal to the rectangular hyperbola xy = 4 at the point P on the hyperbola which is parallel to the line

2x – y = 5 is –

Q2

A tangent to the hyperbola  meets ellipse x2 + 4y2 = 4 in two distinct points. Then the locus of midpoint of this chord is –

Q3

From a point on the line y = x + c, c(parameter), tangents are drawn to the hyperbola  such that chords of contact pass through a fixed point (x1, y1). Then  is equal to –

Q4

If the portion of the asymptotes between centre and the tangent at the vertex of hyperbola  in the third quadrant is cut by the line  being parameter, then –

   

Q5

Find the eccentricity of the hyperbola whose latus rectum is half of its transverse axis.

Q6

For what value of c does not line y = 2x + c touches the hyperbola 16x2 – 9y2 = 144?

Q7

Determiner the equation of common tangents to the hyperbola  and .

Q8

Find the locus of the mid-pints of the chords of the circle x2 – y2 = 16, which are tangent to the hyperbola 9x2 – 16y2 = 144.

Q9

Obtain the equation of a hyperbola with coordinate axes as principal axes given that the distance of one of its vertices from the foci are 9 and 1 units.

Q10

Find the equation to the hyperbola of given transverse axes whose vertex bisects the distance between the center and the focus.