QJEEM16Ma7270: JEE Main 2016 Mathematics - Class 11 JEEM16Ma7270 Solution: A circle passes through (−2, 4) and touches the y-axis at (0,…

EF = perpendicular bisector of chord AB

BG = perpendicular to y-axis

Here C = center of the circle

mid-point of chord AB, D = ( $-$ 1, 3)

slope of AB = ${{4 - 2} \over { - 2 - 0}}$ = $-$ 1

$\because$    EF   $\bot$  AB

$\therefore$    Slope of EF = 1

Equation of EF, y $-$ 3 = 1 (x + 1)

$\Rightarrow$     y = x + 4       . . . .(i)

Equation of BG

y = 2         . . . . (ii)

From equations (i) and (ii)

x = $-$ 2, y = 2

since C be the point of intersection of EF and BG, therefore center, C = ( $-$ 2, 2)

Now coordinates of center C satiesfy the equation

2x $-$ 3y + 10 = 0

Hence 2x $-$ 3y + 10 = 0   is the equation of the diameter