The auxiliary circle of a family of ellipses passes through the origin and makes intercepts of 8 and 6 units on thex- and the y-axis, respectively. If the eccentricity of all such ellipses is 1/2, then the locus of the focus will be

Book Online Demo

Check Your IQ

Try Test

Courses

Dropper NEET Course Dropper JEE Course Class - 12 NEET Course Class - 12 JEE Course Class - 11 NEET Course Class - 11 JEE Course Class - 10 Foundation NEET Course Class - 10 Foundation JEE Course Class - 10 CBSE Course Class - 9 Foundation NEET Course Class - 9 Foundation JEE Course Class -9 CBSE Course Class - 8 CBSE Course Class - 7 CBSE Course Class - 6 CBSE Course

Offline Centres

The auxiliary circle of a family of ellipses passes through the origin and makes intercepts of 8 and 6 units on the
x- and the y-axis, respectively. If the eccentricity of all such ellipses is 1/2, then the locus of the focus will be

see full answer

Start JEE / NEET / Foundation preparation at rupees 99/day !!

21% of IItians & 23% of AIIMS delhi doctors are from Sri Chaitanya institute !!

An Intiative by Sri Chaitanya

$\frac{x^{2}}{16} + \frac{y^{2}}{9} = 25$

none of these

$4 x^{2} + 4 y^{2} - 32 x - 24 y + 75 = 0$

$\frac{x^{2}}{16} + \frac{y^{2}}{36} = 25$

answer is B.

(Unlock A.I Detailed Solution for FREE)

Ready to Test Your Skills?

Check your Performance Today with our Free Mock Test used by Toppers!

Take Free Test

Detailed Solution

The center of the family of ellipse is (4, 3) and the distance of focus from the center is ae = 5/2.

Hence, the locus is $(x - 4)^{2} + (y - 3)^{2} = \frac{25}{4}$

Watch 3-min video & get full concept clarity

Result Producing online coaching for JEE/NEET of south India

Largest All India Test Series for JEE/NEET

Best Books for IIT JEE

Best Books for NEET

How to Join IIT after 10th

Best Courses for You

JEE

NEET

Foundation JEE

Foundation NEET

CBSE

Get Expert Academic Guidance – Connect with a Counselor Today!

Result Producing online coaching for JEE/NEET of south India

Largest All India Test Series for JEE/NEET

Best Books for IIT JEE

Best Books for NEET

How to Join IIT after 10th