Question

A circle passes through the point (-1,7) and touches the line $y=ax$ at (1,1). its diameter is

• A. $4\sqrt{2}$
• B. $5$
• C. $5\sqrt{2}$
• D. 6

Answer 1

Answer: (B)

$5$

The equation of the circle is$(x-1{)}^2+(y-1{)}^2+\lambda (y-2)=0$

It passes through the point $(-1,7)$

$\therefore 40+8\lambda =0\Rightarrow \lambda =-5$

$\therefore$ Circle is $x^2+y^2+3x-7y+12=0$

$\therefore r^2=\frac{9}{4}+\frac{9}{49}-2=\frac{50}{4}$

$\therefore 4r^2=(2r{)}^2=50\therefore 2r=5\sqrt{2}$