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Question

A circle with radius r touches the parabola y2=4x at two points such that area formed by common tangent and common chord is 32 sqaure units. the value of r is

A
5 units
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B
25units
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C
35units
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D
45units
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Solution

The correct option is B 25units

For circle to touch the parabola at two distinct points,the circle should be symmetric to the axis of the parabola as given in the figure

For given parabola y2=4x
a=1

Let B(t2,2t) , C(t2,2t).So, D(t2,0)
Tangents at B,C intersect at A(t2,0)

area of requiredABC=2×12×DB×AD
32=(2t)×(2t2)
t=2

Now, normal at B will pass through the centre of circle

equation of Normal is
y+xt=2t+3
y+2x=4+8
y+2x=12

for y=0
x=6
Hence, centre of circle is (6,0)

Radius of this circle is OB=(64)2+(04)2=4+16=25 units

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