The point(s) on the line x = 2 from which the tangents drawn to the ci

1.	The point(s) on the line x = 2 from which the tangents drawn to the circle x2 + y2 = 16 are at right angles is (are)(a) (2, -2√5) (b) (2, 2√5)(c) (2, 2√7)(d) (2, -2√7)
Answer» Correct option (a,d) Explanation : If the tangents drawn are at right angles, the points must be the intersection of the line x = 2 with the director circle x² + y² = 32 of the circle x² + y² = 16. Substituting x + 2 in x² + y² = 32, we have y² = 28 or y = ±2√7 Therefore, the points are (2, 2√7 ) and (2, -2√7).

The point(s) on the line x = 2 from which the tangents drawn to the circle x2 + y2 = 16 are at right angles is (are)(a) (2, -2√5) (b) (2, 2√5)(c) (2, 2√7)(d) (2, -2√7)

Answer»

Correct option (a,d)

Explanation :

If the tangents drawn are at right angles, the points must be the intersection of the line x = 2 with the director circle x² + y² = 32 of the circle x² + y² = 16. Substituting x + 2 in x² + y² = 32, we have

y² = 28 or y = ±2√7

Therefore, the points are (2, 2√7 ) and (2, -2√7).

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The point(s) on the line x = 2 from which the tangents drawn to the circle x2 + y2 = 16 are at right angles is (are)(a) (2, -2√5) (b) (2, 2√5)(c) (2, 2√7)(d) (2, -2√7)

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