Ask a Doubt

Request a call back

Join NOW to get access to exclusive study material for best results

CBSE Class 11-science Answered

The radius of the circle passing through the two foci and an end point of the minor axis of the ellipse x ²/16 + y ²/25 =1 is ?

Asked by Malavika Umesh | 01 May, 2015, 01:52: PM

Expert Answer

For the ellipse

x squared over 16 plus y squared over 25 equals 1

, the major axis is along Y-axis and the minor axis is along X-axis. (since the denominator of x² term is less)

Here

a squared equals 25 comma space b squared equals 16

c squared equals a squared minus b squared equals 25 minus 16 equals 9

The coordinates of foci are

open parentheses 0 comma space plus-or-minus c close parentheses equals open parentheses 0 comma space plus-or-minus 3 close parentheses

The end points of minor axis are

open parentheses plus-or-minus b comma space 0 close parentheses equals open parentheses plus-or-minus 4 comma space 0 close parentheses

So, we have to form a circle passing through

open parentheses 0 comma space plus-or-minus 3 close parentheses

and one end point of minor axis

open parentheses 4 comma space 0 close parentheses

.

Since, it's an isosceles triangle, the center lies on the perpendicular bisector of

open parentheses 0 comma space plus-or-minus 3 close parentheses

, that is X-axis.

Let the coordinates of the center be

open parentheses p comma 0 close parentheses

.

Equating the square of radii of the circle we get

p squared plus 3 squared equals open parentheses 4 minus p close parentheses squared rightwards double arrow p squared plus 3 squared equals 16 plus p squared minus 8 p rightwards double arrow 8 p equals 7 rightwards double arrow p equals 7 over 8

Hence, radius=

4 minus 7 over 8 equals 25 over 8

Answered by satyajit samal | 03 May, 2015, 10:43: AM

Concept Videos

Practice Test

Webinar

Pre Board Assessment

Answered Unanswered My Questions My Answers

CBSE 11-science - Maths

Find the equation of the ellipse with centre at the origin , major axis on the x- axis and passing through the point (4,3) and (-1,4)..

Asked by Praktu111 | 09 Jun, 2019, 08:18: AM

ANSWERED BY EXPERT

CBSE 11-science - Maths

(1) A circle is concentric with the ellipse (x^2)/(a^2) + (y^2)/(b^2) =1 and passed through the focus F1 and F2 of the ellipse. Two curves intersect at four points. Let P be any point of intersection. If the major axis of the ellipse is 15 and the area of the triangle PF1F2 = 26 , then find the value of 4a^2 - 4b^2 .

Asked by sudhanshubhushanroy | 20 Mar, 2018, 10:12: PM

ANSWERED BY EXPERT

CBSE 11-science - Maths

Find the co-ordiantes of the foci, the vertices, the length of major axis, the minor axis the eccentricity and the length of the latus rectum of the ellipse.

Asked by Topperlearning User | 13 Nov, 2016, 08:09: PM

ANSWERED BY EXPERT

CBSE 11-science - Maths

Asked by Topperlearning User | 25 Apr, 2014, 11:37: AM

ANSWERED BY EXPERT

CBSE 11-science - Maths

Asked by Topperlearning User | 25 Apr, 2014, 11:38: AM

ANSWERED BY EXPERT

CBSE 11-science - Maths

Asked by Topperlearning User | 25 Apr, 2014, 11:38: AM

ANSWERED BY EXPERT

CBSE 11-science - Maths

Asked by Topperlearning User | 25 Apr, 2014, 11:39: AM

ANSWERED BY EXPERT

CBSE 11-science - Maths

Asked by Topperlearning User | 25 Apr, 2014, 11:39: AM

ANSWERED BY EXPERT

CBSE 11-science - Maths

Asked by Topperlearning User | 25 Apr, 2014, 11:40: AM

ANSWERED BY EXPERT

CBSE 11-science - Maths

Find the equation of the ellipse whose major axis is on the x-axis and passes through the points (1,4) and (-6,1)

Asked by Topperlearning User | 25 Apr, 2014, 10:58: AM

ANSWERED BY EXPERT

My Class Videos Tests Plans Ask a Doubt