CircleMedium
Question
The equation of the common tangent touching the circle (x -3)2 + y2 = 9 and the parabola y2 = 4x above the x-axis is
Options
A.√3y = 3x + 1
B.√3y = -(x + 3)
C.√3y = x + 3
D.√3y = -(3x + 1)
Solution
Any tangrnt to y2 = 4x is of the form y = mx + 
, (∵ a = 1) and this touches the circle (x - 3)2 + y2 = 9
If
[∵ Centre of the circle is (3, 0) and radius is 3]
⇒
⇒ 9m2 + 1
⇒ 9m4 + 1 + 6m2 = 9m2 (m2 + 1)
⇒ 9m4 + 1 + 6m2 = 9m4 + 9m2
⇒ 3m2 = 1 ⇒
If the tangent touches the parabola and circle above the x-axis, then slope m should be positive.
∴
and the equation is 
or y = x + 3.
, (∵ a = 1) and this touches the circle (x - 3)2 + y2 = 9 If
[∵ Centre of the circle is (3, 0) and radius is 3]⇒
⇒ 9m2 + 1
⇒ 9m4 + 1 + 6m2 = 9m2 (m2 + 1)
⇒ 9m4 + 1 + 6m2 = 9m4 + 9m2
⇒ 3m2 = 1 ⇒
If the tangent touches the parabola and circle above the x-axis, then slope m should be positive.
∴
and the equation is or y = x + 3.
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