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Offline Centres

In the given figure, the circle $x^{2} + y^{2} = 25$ intersects x–axis at points A and B. The line x = 11 intersects x–axis, at point C. Point P moves along the line x = 11 above the x–axis and AP intersects the circle at Q.
Column–I Column–II
A The coordinates of point P if the $Δ$ AQB has the maximum area is P (11, 0)
B The coordinates of point P if Q is the middle point of AP is Q (11, 8)
C The co–ordinates of P if the area of $Δ$ AQB is 1/4th of the area of $Δ$ APC is R (11, 12)
D The co–ordinates of P if $| A P - B P |$ is maximum S (11, 16)

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$A - Q, B - S, C - R, D - P$

$A - P, B - Q, C - R, D - Q$

$A - S, B - P, C - R, D - Q$

$A - S, B - Q, C - R, D - P$

answer is D.

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Detailed Solution

(a) Q lies on y–axis i.e., OQ = radius

$\frac{y_{P} - 0}{11 - 5} = 1$

$(b) x_{Q} = \frac{11 - 5}{2} = 3$

$y_{Q} = \sqrt{25 - 9} = 4$

$\frac{y_{P} + y_{A}}{2} = 4$

$y_{P} = 8$

$(c) \frac{1}{4} \frac{1}{2} (16) (16 \tan θ) = \frac{1}{2} (10 \cos θ) (10 \sin θ)$

$\cos^{2} θ = \frac{16 \times 16}{4 \times 10 \times 10} = \frac{16}{25}$

$\cos θ = \frac{4}{5}$

$y_{P} = 16 \times \frac{3}{4} = 12$

$(d) y_{P} = 0$

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