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  • Extremities of a diagonal of a rectangle are (0,0) and (4,3). The equations of the tangents to the circumcircle of the rectangle which are parallel to this diagonal are<div class='qna-opti

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

Option: 1

\mathrm{16 x+8 y \pm 25=0}


Option: 2

\mathrm{6 x-8 y \pm 25=0}


Option: 3

\mathrm{8 x+6 y \pm 25=0}


Option: 4

\mathrm{6 x+8 y \pm 25=0}


Answers (1)

best_answer

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

\mathrm{x(x-4)+y(y-3)=0 \text { i.e., } x^2+y^2-4 x-3 y=0}

\mathrm{\text { i.e., }(x-2)^2+\left(y-\frac{3}{2}\right)^2=\left(\frac{5}{2}\right)^2}  ....[i]

m = slope of OA = 3/4 ...(ii)
 Tangents parallel to the diagonal OA are

\mathrm{\begin{aligned} & y-\frac{3}{2}=\frac{3}{4}(x-2) \pm \frac{5}{2} \sqrt{1+\frac{9}{16}} \\ & \text { i.e., } 6 x-8 y \pm 25=0 \end{aligned}}

Posted by

Pankaj Sanodiya

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