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IF THE POINT (1,0) (2,-7) (8,1) AND (9,A) ARE CONCYCLIC. THEN A IS (A)-5 (B)-6 (C)4 (D)6

IF THE POINT (1,0) (2,-7) (8,1) AND (9,A) ARE CONCYCLIC. THEN A IS
(A)-5
(B)-6
(C)4
(D)6

Grade:12

1 Answers

SHAIK AASIF AHAMED
askIITians Faculty 74 Points
6 years ago
Hello student,
Let us find a circle p[assing through points (1,0)(2,-7) and (8,1)
general form of circle isx² + y² + 2gx + 2fy + c = 0
As the points (1,0), (2,-7) and (8,1) lie on it, we get
1+2g+c=0
53+4g-14y+c=0
65+16g+2f+c=0
solving above 3 equations we get g=-5 f=3 c=9
so equation of circle is x² + y² -10x +6y + 9 = 0
As (9,A) lies on above circle we get
81+A2-90+6A+9=0
A(A+6)=0
so A=-6
Thanks and Regards
Shaik Aasif
askIITians faculty

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