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 :
sq. units
sq. units
Text Solution
Verified by ExpertsA
Equation of circle (x + 4)(x – 6) + (y – 4) (y + 1) = 0
⇒ x 2 + y 2 – 2x –3y – 28 = 0 ….(i)
Put x = 0 in (i)
y 2 – 3y – 28 = 0 ⇒ y = 7, y = – 4
A(0, – 4) B(0, 7)
Equation of tangent at A(0, – 4) T = 0
⇒ 2x + 11y + 77 = 0 ….. (ii)
Equation of tangent at B(0, 7) Τ = 0
2x – 11y + 77 = 0 ..... (iii)
sol.(ii) & (iii) C ≡ (–121/4, 3/2)
Δ = 
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