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Question

Radius of the largest circle which passes through the focus of the parabola y2=4x and contained in it is

A
8
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B
4
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C
2
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D
5
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Solution

The correct option is C 4

Let (h,0) be the circle’s center.

Here,

h=1+r

Equation of the circle is,

(xh)2+y2=r2

(x1r)2+y2=r2

x2+y22x2xr+1=0

But, y2=4x (given). Thus, we get

x2+2x2xr+2r+1=0

x2+x(22r)+2r+1=0

The above quadratic equation will have equal roots, because the circle intersects the parabola. So,

(22r)2=4(2r+1)

4+4r28r=8r+4

4r216r=0

r24r=0

r(r4)=0

Radius cannot be zero. So,

r=4

Hence, this is the required result.

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