Question

Tangents are drawn to x² + y² = 16 from the point P(0, h). These tangents meet the x-axis at A and B. If the area of triangle PAB is minimum then

• A. h = 12$\sqrt{2}$
• B. h = 6$\sqrt{2}$
• C. h = 8$\sqrt{2}$
• D. h = 4$\sqrt{2}$

Answer 1

Answer: (D)

h = 4$\sqrt{2}$

Answer 2

Let ∠COA = θ ⇒ OA = OC.secθ = 4 secθ Also ∠OPC = θ ⇒ OP = OC.cosecθ =4cosecθ

Now ∆_PAB = OA.OP = $\frac { 32 } { \sin 2 \theta }$

For ∆_PAB to be minimum sin2 θ = 1 ⇒ θ = $\frac { \pi } { 4 }$

⇒ P = (0, $4 \sqrt { 2 }$)