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Question

Equation of a common tangent to the circle, x2+y26x=0 and the parabola, y2=4x, is
  1. 23y=x12
  2. 23y=12x+1
  3. 3y=x+3
  4. 3y=3x+1


Solution

The correct option is C 3y=x+3
The curves are y2=4x
and x2+y26x=0(x3)2+y2=9 
Equation of tangent to y2=4x is
y=mx+1m     ...(1)
Equation of tangent to the circle is
y=m(x3)+31+m2,
where m is the slope.
Since the two curves have common tangents,
mx+1m=m(x3)+31+m2
m=±13

Putting the value of m in (1), we get
3y=±(x+3)
i.e., 3y=x+3 
 

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