Application of DerivativeHard
Question
The coordinates of the point of the parabola y2 = 8x , which is at minimum distance from the circlex2 + (y + 6)2 = 1 are
Options
A.(2 , - 4)
B.(18 , -12)
C.(2 , 4)
D.none of these
Solution
P1 : y2 = 8x
C1 : x2 + (y + 6)2 = 1
Equation of normal of parabola
y = mx - 2am - am3
if passes through (0,- 6)
- 6 = - 2am - am3
∵ a = 2
3 = 2m + m3
m3 + 2m - 3 = 0 ⇒ m = 1.
Point on parabola (am2 , -2am) ≡ (2, -4).
C1 : x2 + (y + 6)2 = 1
Equation of normal of parabola
y = mx - 2am - am3
if passes through (0,- 6)
- 6 = - 2am - am3
∵ a = 2
3 = 2m + m3
m3 + 2m - 3 = 0 ⇒ m = 1.
Point on parabola (am2 , -2am) ≡ (2, -4).
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