JEE Mains · Maths · STD 11 - 10.1 circle and system of circle
Let the tan gents drawn to the circle, \(x^2 + y^2 = 16\) from the point \(P(0, h)\) meet the \(x-\) axis at point \(A\) and \(B.\) If the area of \(\Delta APB\) is minimum, then \(h\) is equal to
- A \(4\sqrt 2\)
- B \(3\sqrt 3\)
- C \(3\sqrt 2\)
- D \(4\sqrt 3\)
Answer & Solution
Correct Answer
(A) \(4\sqrt 2\)
Step-by-step Solution
Detailed explanation
\(OP = \frac{4}{{\sin \,\theta }}\) \(OB = \frac{4}{{\cos \,\theta }}\) Area \( = OP \times OB = \frac{{16}}{{\sin \,\theta \,\cos \,\theta \,}} = \frac{{32}}{{\sin \,2\theta }}\) least value \(\sin \,2\theta = 1;\theta = {45^0}\) So,…
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