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Question

The equation of the common tangent touching the circle (x3)2+y2=9 and the parabola y2=4x above the X-axis is

A
3y=3x+1
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B
3y=(x+3)
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C
3y=x+3
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D
3y=(3x+1)
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Solution

The correct option is C 3y=x+3
Any tangent to y2=4x is of the form y=mx+1m, (a=1) and this touches the circle (x3)2+y2=9.
If m(3)+1m0m2+1=3
[ centre of the circle is (3, 0) and radius is 3].
3m2+1m=±3m2+1
3m2+1=±3mm2+1
9m4+1+6m2=9m2(m2+1)
3m2=1
m=±13
If the tangent touches the parabola and circle above the X-axis, then slope m should be positive.
m=13 and the equation is y=13x+3
or 3y=x+3.

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