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Question

Extremities of a diagonal of a rectangle are (0,0) and (4,3). The equation of the tangents to the circumcircle of the rectangle which are parallel to this diagonal are

A
16x+8y±25=0
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B
6x8y±25=0
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C
8x+6y±25=0
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D
None of these
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Solution

The correct option is B 6x8y±25=0
Extremities of the diagonal OA of the rectangle are O(0,0) and A(4,3). then, OA is the diameter of the circumcircle, so equation of the circumcircle is
x(x4)+y(y3)=0i.e., x2+y24x3y=0
i.e., (x2)2+(y32)2=(52)2 ...(1)
m= slope of OA=34 ...(2)
Tangents parallel to the diagonal OA are
y32=34(x2)±521+916
i.e., 6x8y±25=0.

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