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Byju's Answer

Standard XIII

Mathematics

Director Circle

If the radius...

Question

If the radius of the circumcircle of the triangle $T P Q$ , where $P Q$ is chord of contact corresponding to point $T$ with respect to circle $x^{2} + y^{2} - 2 x + 4 y - 11 = 0$ , is $6$ units, then minimum distance of $T$ from the director circle of the given circle is

6

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12

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6 \sqrt{2}

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12 - 4 \sqrt{2}

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Solution

The correct option is D $12 - 4 \sqrt{2}$
Given circle
$(x - 1)^{2} + (y + 2)^{2} = 16$
Its director circle is
$(x - 1)^{2} + (y + 2)^{2} = 32$
$∴ O S = 4 \sqrt{2}$

Therefore, required distance,
$T S = O T - S O = 12 - 4 \sqrt{2}$

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Similar questions

Q. If the radius of the circumcircle of the triangle TPQ where PQ is chord of contact corresponding to point T with respect to circle

x^{2} + y^{2} - 2 x + 4 y - 11 = 0

6

units then distance of T from the director circle of the given circle is

Q. If the radius of the circumcircle of the triangle TPQ, where PQ is chord of contact corresponding to point T with respect to circle

x^{2} + y^{2} - 2 x + 4 y - 11 = 0

, is

12

units, then minimum distance of

T

from the director circle of the given circle is

Q. If the radius of the circumcircle of the triangle

T P Q

, where

P Q

is chord of contact corresponding to point

T

with respect to circle

x^{2} + y^{2} - 2 x + 4 y - 11 = 0

, is

6

units, then minimum distance of

T

from the director circle of the given circle is

Q. If the chord of contact of the circle

x^{2} + y^{2} - 2 x + 4 y + λ = 0

with respect to a point lying on the circle

x^{2} + y^{2} - 2 x + 4 y + 1 = 0

touches the circle

x^{2} + y^{2} - 2 x + 4 y + 3 = 0

, then the number of value(s) of

λ

Tangents are drawn from the point P(1, 8) to the circle $x^{2} + y^{2} - 6 x - 4 y - 11 = 0$ touch the circle at the point A and B, then equation of the circumcircle of the triangle PAB is

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If the radius of the circumcircle of the triangle TPQ, where PQ is chord of contact corresponding to point T with respect to circle x2+y2−2x+4y−11=0, is 6 units, then minimum distance of T from the director circle of the given circle is

The correct option is D 12−4√2Given circle (x−1)2+(y+2)2=16 Its director circle is (x−1)2+(y+2)2=32 ∴OS=4√2 Therefore, required distance, TS=OT−SO=12−4√2

If the radius of the circumcircle of the triangle $T P Q$ , where $P Q$ is chord of contact corresponding to point $T$ with respect to circle $x^{2} + y^{2} - 2 x + 4 y - 11 = 0$ , is $6$ units, then minimum distance of $T$ from the director circle of the given circle is

The correct option is D $12 - 4 \sqrt{2}$
Given circle
$(x - 1)^{2} + (y + 2)^{2} = 16$
Its director circle is
$(x - 1)^{2} + (y + 2)^{2} = 32$
$∴ O S = 4 \sqrt{2}$

Therefore, required distance,
$T S = O T - S O = 12 - 4 \sqrt{2}$