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How to find the equation common tangents of parabola y^2=4x and circle x^2 + y^2 = 1?

How to find the equation common tangents of parabola y^2=4x and circle x^2 + y^2 = 1?

Grade:12

1 Answers

Vikas TU
14149 Points
6 years ago

focal point of circle: (0,0) 
Condition of digression on parabola: 
y=mx+a/m 
a=1 
y=mx+1/m 
Opposite Distance from the focal point of the circle = 0 
|3m+1/m|/(1+m)1/2=3 
m2=1/3 => m=+1/√3 or - 1/√3 
As digression is above x-hub, slant is (+)ve 
In this manner, Equation of digression: 
y=x/√3+√3 

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