Browse by Stream
QnA
Home
QnA
Go To Your Study Dashboard

Get Answers to all your Questions

header-bg qa
  • Home
  • Engineering
  • If the equation of the diameter of the circle  is <img alt="y+x=0" src="https://learn.caree

If the equation of the diameter of the circle x^2+y^2=1 is y+x=0 then find the equation of system of parallel chords which is perpendicular to diameter?

Option: 1

y=x+c for all value of c


Option: 2

y=x+c for -1 \leq c\leq1


Option: 3

y=x+c For  -2 < c <2


Option: 4

Can't calculate


Answers (1)

best_answer

 

 

DIAMETER OF A CIRCLE -

 DIAMETER OF A CIRCLE

The locus of the mid-points of a system of parallel chords of a circle is known as the diameter of the circle. 

The diameter of a circle always passes through the centre of a circle and perpendicular to the parallel chords

\\\mathrm{Let\;the\;equation\;of\;the\;circle\;be\;\;x^2+y^2=a^2\;\;and\;equation\;of}\\\mathrm{parallel\;chord\;AB\;is,\;\;y=mx+c.}

Equation of any diameter to the given circle is perpendicular to the given parallel chord is my + x + λ = 0 which passes through the centre (0, 0) of a circle.

m?0 + 0 +  λ = 0

 λ = 0

Hence, the required equation of the diameter is x + my = 0

-

 

 

Given circle 

x^2+y^2=1

Equation of diameter y+x=0 

Equation of the system of parallel chords 

y=x+c

from the above figure 

y=x+c

\text{Equation of above tangents }\\ \frac{x}{2}-\frac{y}{2}=1\\- \frac{x}{2}-\frac{y}{2}=1

-2 < c <2

Posted by

Divya Prakash Singh

View full answer

JEE Main high-scoring chapters and topics

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

Similar Questions