Question
Question: The equation of common tangent to the curves y<sup>2</sup> = 8x and xy = –1 is...
The equation of common tangent to the curves y2 = 8x and
xy = –1 is
A
3y = 9x + 2
B
y = 2x + 1
C
2y = x + 8
D
y = x + 2
Answer
y = x + 2
Explanation
Solution
Any tangent is y = mx +
Ž y = mx + 
.
If it is tangent to xy = –1 then it will cut at two coincident points.
\ x
+ 1 = 0 Ž m2x2 + 2x + m = 0
D = 0 ; 4 – 4m3 = 0 Ž m = 1 so y = x + 2