Browse by Stream
QnA
Home
QnA
Go To Your Study Dashboard

Get Answers to all your Questions

header-bg qa
  • Home
  • Engineering
  • The directrix of an ellipse with eccentricity  <img alt="\mathrm {\frac{1}{\sqrt{2}}}" src="https://entrancecorner.oncodecogs.com/gif.latex?%5Cmathrm%20%7B%5Cfrac%7B1%7D%7B%5Csqrt%7B2%7D%

The directrix of an ellipse with eccentricity  \mathrm {\frac{1}{\sqrt{2}}} is   \mathrm {\: \: \: \: x+y=1}  If the corresponding focus is  (1,2) , then the length of the minor axis is
 

Option: 1

\sqrt{2}


Option: 2

2


Option: 3

2 \sqrt{2}


Option: 4

4


Answers (1)

best_answer

The distance of  \mathrm S(1,2)  from the directrix

\begin{aligned} &\mathrm { x+y=1 \text { is } \frac{1+2-1}{\sqrt{2}}=\sqrt{2} }\\ & \mathrm {\therefore \quad \frac{a}{e}-a e=\sqrt{2} \Rightarrow \sqrt{2} a-\frac{a}{\sqrt{2}}=\sqrt{2} \Rightarrow a=2} \\ &\mathrm { 2 b=2 a \sqrt{1-e^2}=4 \sqrt{1-\frac{1}{2}}=2 \sqrt{2}} . \end{aligned}

Posted by

SANGALDEEP SINGH

View full answer

JEE Main high-scoring chapters and topics

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

Similar Questions

Trending Articles/News

anam-khan

JAC Chandigarh Counselling 2025: Round 1 seat allotment result out for BTech admissions
anam-khan

JoSAA round 5 seat allotment result 2025 out on josaa.nic.in
anam-khan

BTech aspirant from north-east or UT? Apply for CSAB NEUT counselling 2025 today

Latest Question