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Q.

Let AB be the chord $4 x - 3 y + 5 = 0$ with respect to the circle $x^{2} + y^{2} - 2 x + 4 y - 20 = 0.$ If $C = (7, 1),$ then the area of the triangle ABC is

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a

20 sq.units

b

45 sq.units

c

24 sq.units

d

15 sq.units

answer is C.

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Detailed Solution

$A B =$ length of chord $= 8$
$h =$ distance from $(7, 1)$ to AB $= 6$
Area $= \frac{1}{2} (8) (6) = 24$

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