Application of DerivativeMedium
Question
The equation of the common tangent to the curves y2 = 8x and xy = - 1 is
Options
A.3y = 9x + 2
B.y = 2x +1
C.2y = x + 8
D.y = x + 2
Solution
Tangent to the curve y2 = 8x is y = 
. So it must satisfy xy = -1.
x
= - 1 ⇒ 
x + 1 = 0
Since it has equal roots, therefore D = 0
⇒
- 4m = 0
⇒ m3 = 1 ⇒ m = 1
So equation of common tangent is y = x + 2
. So it must satisfy xy = -1.x
= - 1 ⇒ x + 1 = 0Since it has equal roots, therefore D = 0
⇒
- 4m = 0⇒ m3 = 1 ⇒ m = 1
So equation of common tangent is y = x + 2
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