Statement-1 : An equation of a common tangent to the parabola y 2 = 
x and the ellipse 2x 2 + y 2 = 4 is y = 2x + 
.
Statement-2 : If the line y = mx + 
, (m ≠ 0) is a common tangent to the parabola y 2 = 
x and the ellipse 2x 2 + y 2 = 4, then m satisfies m 4 + 2m 2 = 24.
Text Solution
Verified by ExpertsB
Equation of tangent to the ellipse = 
1 is
y = mx ± 
.....
equation of tangent to the parabola y 2 = 16 
x
is y = m x + 
.....
On comparing and
= ± 
⇒ 48 = m 2 (2m 2 + 4) ⇒ 2m 4 + 4m 2 – 48 = 0
⇒ m 4 + 2m 2 – 24 = 0 ⇒ (m 2 + 6) (m 2 – 4) = 0
⇒ m 2 = 4 ⇒ m = ± 2
⇒ equation of common tangents are y = ± 2x ± 2
statement -1 is true.
statement-2 is obviously true.
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