Question bank/JEE Main/Mathematics

What will be the equation of circle whose centre is (3,-1) and
which intercept chord of 6 unit length on straight line
$2x - 5y + 18 = 0$
ml o`Ùk dk lehdj.k ftl Unz (3, - 1) gS rFkk js[kk 2x - 5y + 18
= 0 ij 6 bdkbZ yEckbZ

A$x^{2} + y^{2} - 6x + 2y - 28 = 0$B$x^{2} + y^{2} - 6x + 2y + 1 = 0$C$x^{2} + y^{2} - 6x + 2y - 1 = 0$D$x^{2} + y^{2} - 6x + 2y - 12 = 0$

Show answer and solution▾

$AM = MB = 3$
$CM = \frac{2(3) - 5( - 1) + 18}{\sqrt{2^{2} + 5^{2}}} = \sqrt{29}$
$\Rightarrow R^{2} = CA^{2} = AM^{2} + CM^{2} = 3^{2} + 29 = 38$
Equation of circle is o`Ùk dk lehdj.k
$(x - 3)^{2} + (y + 1)^{2} = R^{2} = 38 \Rightarrow x^{2} + y^{2} - 6x + 2y = 28$

Source: Grass-G / M-25 Mathematics Paper 7 Jan.docx