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The radius of a circle, having minimum a...

The radius of a circle, having minimum area, which touches the curve `y=4-x^2` and the lines `y=|x|` is :

A

`2(sqrt2+2)`

B

`2(sqrt2-1)`

C

`4(sqrt2-1)`

D

`4(sqrt2+1)`

Text Solution

Verified by Experts

The correct Answer is:
C
Let r be the radius of circle. Due to symmetry the centre of the circle lies on y-axis. The circle touches the lines `y=+-x`.

`"In "DeltaOPC, /_COP=pi/4`
`:." "OP=CP=r" and "OC=sqrt2r`.
Now,
`"OR=OC+CR"rArr4=sqrt2r+rrArrr=4/(sqrt2+1)=4(sqrt2+1)`
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OBJECTIVE RD SHARMA ENGLISH-PARABOLA-Section I - Solved Mcqs
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  2. The radical centre of the circles drawn on the focal chords of y^(2)=4...

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  3. For each parabola y=x^(2)+px+q, meeting coordinate axes at 3-distinct ...

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  4. Let A(x(1),y(1)) and B(x(2),y(2)) be two points on the parabola y^(2) ...

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  5. Let A and B be two distinct points on the parabola y^2=4x. If the ax...

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  6. the shortest distance between the line y-x=1 and the curve x=y^(2) ...

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  7. about to only mathematics

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  8. Let PQ be a focal chord of the parabola y^(2)=4ax. The tangents to the...

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  9. Let a, r, s, t be non-zero real numbers. Let P(at^(2),2at),Q(ar^(2),2a...

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  10. Let a, r, s, t be non-zero real numbers. Let P(at^(2),2at),Q(ar^(2),2a...

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  11. Let P and Q be distinct points on the parabola y^2 = 2x such that a c...

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  12. about to only mathematics

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  13. PSQ is a focal chord of a parabola whose focus is S and vertex is A. P...

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  14. Let P be the point on the parabola y^(2)4x which is at the shortest di...

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  15. Let P be the point on the parabola, y^(2)=8x which is at a minimum dis...

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  16. P and Q are two distinct points on the parabola, y^2 = 4x with paramet...

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  17. Let PQ be a focal chord of the parabola y^(2)=4x. If the centre of a c...

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  18. The centres of those circles which touch the circle, x^(2)+y^(2)-8x-8y...

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  19. The radius of a circle, having minimum area, which touches the curve...

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  20. If a chord , which is not a tangent of the parabola y^2=16x has the eq...

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