Question

The extremities of the diagonal of a rectangle are (– 4, 4) and (6, –1). A circle circumscribes the rectangle and cuts intercept a length AB on the y-axis. The area of the triangle formed by AB and the tangents to the circle at A and B is :

• A. $\frac { 1331 } { 8 }$sq. units
• B. $\frac { 763 } { 8 }$ sq. units
• C. 303 sq. units
• D. None of these

Answer 1

Answer: (A)

$\frac { 1331 } { 8 }$sq. units

Answer 2

Equation of circle (x + 4)(x – 6) + (y – 4) (y + 1) = 0

Ž x² + y² – 2x –3y – 28 = 0 ….(i)

Put x = 0 in (i)

y² – 3y – 28 = 0 Ž y = 7, y = – 4

A(0, – 4) B(0, 7)

Equation of tangent at A(0, – 4) T = 0

Ž 2x + 11y + 77 = 0 ….. (ii)

Equation of tangent at B(0, 7) T = 0

2x – 11y + 77 = 0 ..... (iii)

sol.(ii) & (iii) C ŗ (–121/4, 3/2)

D = $\frac { 1 } { 2 } \left| \begin{array} { c c c } \frac { - 121 } { 4 } & \frac { 3 } { 4 } & 1 \\ 0 & 7 & 1 \\ 0 & - 4 & 1 \end{array} \right|$