Get Answers to all your Questions

header-bg qa

A circle cuts a chord of length 4a on the x-axis and passes through a point on the y-axis, distant 2b from the origin. Then the locus of the center of this circle, is:

  • Option 1)

    an ellipse

  • Option 2)

    a parabola

  • Option 3)

    a straight line

  • Option 4)

    a hyperbola

Answers (1)

best_answer

 

Locus -

Path followed by a point p(x,y) under given condition (s).

- wherein

It is satisfied by all the points (x,y) on the locus.

 

 

General form of a circle -

x^{2}+y^{2}+2gx+2fy+c= 0
 

- wherein

centre = \left ( -g,-f \right )

radius = \sqrt{g^{2}+f^{2}-c}

 

Equation of Circle  x^{2}+y^{2}+2gx+2fy+c=0

passes through (0 , 2b )

=>4b^{2}+4f+c=0.......................(1)

=>2\sqrt{g^{2}-c}=4a..........................(2)

=>{g^{2}-c}=4a^{2}

=>{c}=g^{2}-4a^{2}

Putting in (1)

=>4b^{2}+4f+g^{2}-4a^{2}=0

=>x^{2}+4y+4(b^{2}-a^{2})=0

which is equation of parabola.

 

 

 


Option 1)

an ellipse

Option 2)

a parabola

Option 3)

a straight line

Option 4)

a hyperbola

Posted by

admin

View full answer

JEE Main high-scoring chapters and topics

Study 40% syllabus and score up to 100% marks in JEE