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JEE Main 20202 SeptemberMorning Shift
Exam
JEE Main
Year
2020
Date
2 September
Shift
Morning Shift
Subject
Mathematics
Chapter
Circle

JEE Main 2020 · 2 September · Morning Shift · Mathematics · Circle

The numbers of integral values of k for which the line, 3x + 4y = k...

The numbers of integral values of kk for which the line, 3x+4y=k3x + 4y = k intersects the circle, x2+y2−2x−4y+4=0{x}^{2} + {y}^{2} - 2x - 4y + 4 = 0 at two distinct points is....

Correct answer

9

Step-by-step solution

If distance from center to line is less than radius then line cut circle at two distinct point.

Center of circle (1,2),r=1( 1, 2 ) , r = 1

\left|\dfrac{3 + 8 - k}{5}\right| < 1</p><p>∣11−k∣<5</p><p>\left|11 - k\right| < 5

−5<11−k<5⇒k∈(6,16)- 5 < 11 - k < 5 ⇒ k \in ( 6, 16 )

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

Number of values of k=9k = 9.

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