Email
Chat with tutor
logo

Ask Questions, Get Answers

X
 
Questions  >>  CBSE XI  >>  Math  >>  Conic Sections
Answer
Comment
Share
Q)

The equation of a circle with origin as centre and passing through the vertices of an equilateral triangle whose median is of length $3a$ is

[Hint : Centroid of the triangle coincides with the centre of the circle and the radius of the circle is $\large\frac{2}{3}$ of the length of the median]

$\begin{array}{1 1}x^2+y^2=9a^2\\x^2+y^2=16a^2\\x^2+y^2=4a^2\\x^2+y^2=a^2\end{array} $

1 Answer

Comment
A)
Toolbox:
  • Equation of a circle passing through the origin is $x^2+y^2=a^2$
Answer : $x^2+y^2=4a^2$
If the centroid of the triangle coincides with the centre of the circle,then the radius of the circle is $\large\frac{2}{3}$ of the length of the median.
$\therefore r=\large\frac{2}{3}$$\times 3a$
$\Rightarrow r^2=4a^2$
Hence the equation of the circle is $x^2+y^2=4a^2$
Help Clay6 to be free
Clay6 needs your help to survive. We have roughly 7 lakh students visiting us monthly. We want to keep our services free and improve with prompt help and advanced solutions by adding more teachers and infrastructure.

A small donation from you will help us reach that goal faster. Talk to your parents, teachers and school and spread the word about clay6. You can pay online or send a cheque.

Thanks for your support.
Continue
Please choose your payment mode to continue
Home Ask Homework Questions
Your payment for is successful.
Continue
Clay6 tutors use Telegram* chat app to help students with their questions and doubts.
Do you have the Telegram chat app installed?
Already installed Install now
*Telegram is a chat app like WhatsApp / Facebook Messenger / Skype.
...