Question

The equation of the circle which passes through the points (2, 3) and (4, 5) and the centre lies on the straight line y – 4x + 3 = 0, is

• A.
• B.
• C.
• D.

Answer 1

The correct option is B

Required circle is $s+\lambda L=0$

$\Rightarrow (x-2)(x-4)+(y-3)(y-5)+\lambda (x-y+1)=0$

$\Rightarrow x^2+y^2+(\lambda -6)x-(8+\lambda )y+23+\lambda =0$

centre = $(\frac{6-\lambda }{2},\frac{8+\lambda }{2})$

centre lies on y - 4x + 3 = 0

$\Rightarrow \left(\frac{8+\lambda }{2}\right)-4\left(\frac{6-\lambda }{2}\right)+3=0\Rightarrow 8+\lambda -24+4\lambda +6=0\Rightarrow \lambda =2$
$\therefore$ Required circle is
$x^2+y^2-4x-10y+25=0$