Let A and B be two distinct points on the parabola y2=4 x. If the axis of the parabola touches a circle of radius r having AB as its diameter, then the slope of the line joining A and B can be

Question

Let A and B be two distinct points on the parabola y2=4 x. If the axis of the parabola touches a circle of radius r having AB as its diameter, then the slope of the line joining A and B can be (A) -(1/r) (B) (1/ r ) (C) (2/ r ) (D) -(2/r)

Tardigrade Admin · Accepted Answer

A =( t 12, 2 t 1), B =( t 22, 2 t 2) Centre =[( t 12+ t 22/2),( t 1+ t 2)] t 1+ t 2=± r m =(2( t 1- t 2)/ t 12- t 22)=(2/ t 1+ t 2)=± (2/ r )

Q. Let $A$ and $B$ be two distinct points on the parabola $y^{2} = 4 x$ . If the axis of the parabola touches a circle of radius $r$ having $A B$ as its diameter, then the slope of the line joining $A$ and $B$ can be

$- \frac{1}{r}$

$\frac{1}{r}$

$\frac{2}{r}$

$- \frac{2}{r}$

$A = (t_{1}^{2}, 2 t_{1}), B = (t_{2}^{2}, 2 t_{2})$
Centre $= [\frac{t _{1}^{2} + t _{2}^{2}}{2}, (t_{1} + t_{2})]$
$t_{1} + t_{2} = \pm r$
$m = \frac{2 ( t _{1} - t _{2} )}{t _{1}^{2} - t _{2}^{2}} = \frac{2}{t _{1} + t _{2}} = \pm \frac{2}{r}$

Q. Let A and B be two distinct points on the parabola y2=4x. If the axis of the parabola touches a circle of radius r having AB as its diameter, then the slope of the line joining A and B can be

−r1​

r1​

r2​

−r2​