Let the common tangents to the curves 4(x 2 + y 2 ) = 9 and y 2 = 4x intersect at the point Q. Let an ellipse, centered at the origin O, has lengths of semi-minor and semi-major axes equal to OQ and 6, respectively. If e and 
respectively denote the eccentricity and the length of the latus rectum of this ellipse, then 
is equal to___________.
Text Solution
Verified by Experts4
(4)
y=4x
Equation tangent in slope form
…(1)
…(2)
compare (1) & (2)
9m 2 (l + m 2 ) = 4
9m 4 + 9m 2 -4 = 0
9m 4 +12m 2 -3m 2 -4 = 0
3m 2 (3m 2 + 4) - (3m 2 + 4) = 0 .,
m 2 = 
(Rejected)
Equation of common tangent
on X axis y = 0
OQ = -3
b = |OQ| = 3
a = 6
──────────────────────────────────────────────────────────────────────────────────────────
Prepare Smarter with CGP Edu
Get practice questions, solutions, and test series in one place.
Write a Review
Share your experience with this question and solution.
Commentary
Send your comment, doubt, correction, or feedback to admin.
Similar Questions
Explore conceptually related problems