Question
Question: The equation of common tangent to the parabolas y2 = 4ax and x2 = 4by is...
The equation of common tangent to the parabolas y2 = 4ax and x2 = 4by is
A
a1/3x + b1/3y + (ab) = 0
B
a1/3x + b1/3y + (ab)2/3 = 0
C
b1/3x + a1/3y + (ab)1/3 = 0
D
b1/3x – a1/3y – (ab)1/3 = 0
Answer
a1/3x + b1/3y + (ab)2/3 = 0
Explanation
Solution
Tangent of parabola y2 = 4ax is y = mx + a/m, which also touches to the parabola
x2 = 4by ̃ a/m = – bm2 ̃ m = –(a/b)1/3