Browse by Stream
QnA
Home
QnA
Go To Your Study Dashboard

Get Answers to all your Questions

header-bg qa
  • Home
  • Engineering
  • The number of integral values of k for which the line, intersects the circle, <img alt="x^{2}+y^{2}-2x-4y+4=0" src="https://entrancecorner.codecogs.com/gif.lat

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 point is_______.
Option: 1 4
Option: 2 9
Option: 3 14
Option: 4 21

Answers (1)

best_answer

\\\text { Circle } x^{2}+y^{2}-2 x-4 y+4=0 \\ \Rightarrow(x-1)^{2}+(y-2)^{2}=1

Center = (1,2) ; Radius = 1

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

distance of centre from the line < radius

\begin{aligned} &\Rightarrow\left|\frac{3 \times 1+4 \times 2-\mathrm{k}}{\sqrt{3^{2}+4^{2}}}\right|<1\\ &\Rightarrow|11-k|<5\\ &\Rightarrow 6<\mathrm{k}<16\\ &\Rightarrow \mathrm{k} \in\{7,8,9, \ldots \ldots 15\} \text { since } \mathrm{k} \in \mathrm{I}\\ &\text { Number of } \mathrm{K} \text { is } 9 \end{aligned}

Posted by

himanshu.meshram

View full answer

JEE Main high-scoring chapters and topics

Study 40% syllabus and score up to 100% marks in JEE

Similar Questions

Latest Question