Published by:
CGP EDU Academic Team
Published on: August 13, 2026
A common tangent to 9x 2 – 16y 2 = 144 and x 2 + y 2 = 9 is -
A
y = 
+ 
+
B
y = 3 
x + 
x +
C
y = 2 
x + 
x +
D
None of these
Text Solution
Verified by ExpertsThe correct answer is:
B
Let y = mx + c be a common tangent to
9x 2 – 16y 2 = 144 and x 2 + y 2 = 9.
Since, y = mx + c is a tangent to 9x 2 – 16y 2 = 144, therefore,
c 2 = a 2 m 2 – b 2 ⇒ c 2 = 16m 2 – 9 … (1)
Now, y = mx + c is a tangent to x 2 + y 2 = 9, therefore,
= 3 ⇒ c 2 = 9(1 + m 2 ) … (2)
From equations (1) and (2), we get
16m 2 – 9 = 9 + 9m 2 ⇒ m = ± 3 
On putting the value of m in equation (2), we get c = ± 
Hence, y = 3 
x + 
is a common tangent.
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