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The number of integral values of k for which the line, 3x + 4y = k intersects the circle, x^2 + y^2–2x – 4y + 4 = 0 at two distinct points is

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The number of integral values of k for which the line, 3x + 4y = k intersects the circle, x2 + y2–2x – 4y + 4 = 0 at two distinct points is ......

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Circle x2 + y2 – 2x – 4y + 4 = 0

⇒ (x – 1)2 + (y – 2)2 = 1

Centre : (1, 2)     radius = 1

line 3x + 4y – k = 0 intersects the circle at two distinct points.

⇒ distance of centre from the line < radius

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