Question

The equation of a common tangent to the parabolas y = x2 and y = –(x – 2)2 is

• A. y = 4(x – 2)
• B. y = 4(x – 1)
• C. y = 4(x + 1)
• D. y = 4(x + 2)

Answer 1

Answer: (B)

y = 4(x – 1)

Answer 2

The correct answer is (B) : y = 4(x – 1)
Equation of tangent of slope m to y = x2
$y=mx−\frac{1}{4}m^2$
Equation of tangent of slope m to y = –(x – 2)2
$y=m(x−2)+\frac{1}{4}m^2$
If both equation represent the same line
$\frac{1}{4}m^2−2m=−\frac{1}{4}m^2$
m = 0, 4
So, equation of tangent
$y = 4x-4$