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Q.

PQ is a double ordinate of the parabola y2=4x which passes through the focus S. ΔPQA is isosceles right angled triangle where A is on the axis of the parabola. Line PA meets the parabola at C and QA meets the parabola at B. Which of the following statement(s) is(are) CORRECT.

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a

Circum radius of trapezium PBCQ is 40

b

Ratio of inradius of ΔABC and that of ΔPAQ is 3 : 1

c

Area of the trapezium PBCQ is 64 Sq. units

d

Circum radius of trapezium PBCQ is 36

answer is A, C, D.

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Detailed Solution

P(1,2)Q(1,2) 
Question Image 
ΔPAQ is right
Angled isosceles
Slope of PA = –1, QA = 1
Equation of PA is x + y – 3 = 0
Equation of QB is x – y – 3 = 0
On solving with parabola we get B, C as (9, 6), (9,  6) respectively
Area of trapezium PBCQ = 64
Circum radius of PBCQ=210 
In radius of ΔAPQ=21  
In radius of ΔABC=3(21)

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