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JEE Main 201815 AprilMorning ShiftOnline
Exam
JEE Main
Year
2018
Date
15 April
Shift
Morning Shift
Mode
Online
Subject
Mathematics
Chapter
Circle

JEE Main 2018 · 15 April · Morning Shift · Online · Mathematics · Circle

A circle passes through the points (2,3) and (4 , 5). If its centre...

A circle passes through the points (2,3)(2,3) and (4(4, 5). If its centre lies on the line, y−4x+3=0y-4 x+3=0, then its radius is equal to

Options

  1. A5\sqrt{5}
  2. B1
  3. C2\sqrt{2}
  4. D2

Correct answer

C. 2\sqrt{2}

Step-by-step solution

Equation of the line passing through the points (2,3)and(4,5)(2,3) and (4,5) is y-3=(5−34−2)\left(\frac{5-3}{4-2}\right)x-2 \Rightarrow x-y+1=0 Equationoftheperpendicularlinepassingthroughthemidpoint(3,4)of the perpendicular line passing through the midpoint(3,4) is x+y−7=0x+y-7=0 Lines (1) and (2) intersect at the center of the circle. So, the center of the circle is (3,4)(3,4) Therefore, the radius is (x2−x1)2+(y2−y1)2=(2−3)2+(3−4)2=2 units. \begin{aligned}&\sqrt{\left(x_2-x_1\right)^2+\left(y_2-y_1\right)^2}\\ &=\sqrt{(2-3)^2+(3-4)^2}=\sqrt{2} \text{ units. } \end{aligned}
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