If the circles x2 + y2 – 16x – 20y + 164 = r2 (x – 4)2 + (y –

1.	If the circles x2 + y2 – 16x – 20y + 164 = r2 (x – 4)2 + (y – 7)2 = 36 intersect at two distinct points, then : (1) r > 11 (2) 0 < r < 1 (3) 1 < r < 11 (4) r = 11
Answer» The correct option (3) 1 < r < 11 Explanation: (x – 8)² + (y – 10)² = r² ; (x – 4)² + (y – 7)² = 36 C₁(8, 10); C₂(4, 7) : \|r – 6\| < C₁C₂ < \|r\| + 6 ⇒ \|r – 6\| < 5 < \|r\| + 6 ⇒ r ∈ (1, 11)

If the circles x2 + y2 – 16x – 20y + 164 = r2 (x – 4)2 + (y – 7)2 = 36 intersect at two distinct points, then : (1) r > 11 (2) 0 < r < 1 (3) 1 < r < 11 (4) r = 11

Answer»

The correct option (3) 1 < r < 11

Explanation:

(x – 8)² + (y – 10)² = r² ; (x – 4)² + (y – 7)² = 36

C₁(8, 10); C₂(4, 7) : |r – 6| < C₁C₂ < |r| + 6

⇒ |r – 6| < 5 < |r| + 6 ⇒ r ∈ (1, 11)

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If the circles x2 + y2 – 16x – 20y + 164 = r2 (x – 4)2 + (y – 7)2 = 36 intersect at two distinct points, then : (1) r &gt; 11 (2) 0 &lt; r &lt; 1 (3) 1 &lt; r &lt; 11 (4) r = 11

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If the circles x2 + y2 – 16x – 20y + 164 = r2 (x – 4)2 + (y – 7)2 = 36 intersect at two distinct points, then : (1) r > 11 (2) 0 < r < 1 (3) 1 < r < 11 (4) r = 11