Question

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 ______.

पर्याय

• 6.00

• 7.00

• 8.00

• 9.00

Answer 1

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 9.00.

Explanation:

x² + y² – 2x – 4y + 4 = 0

C(1, 2)

r = `sqrt(1 + 4 - 4)` = 1

Lines 3x + 4y – k = 0

Distance from center < Radius line

`|(3 + 8 - k)/sqrt(3^2 + 4^2)| < 1`

|11 – k| < 5

–5 < 11 – k < 5

–16 < –k < –6

⇒ 6 < k < 16

k = 7, 8, 9, 10, 11, 12, 13, 14, 15

Total 9 values