Question

The focal chord to $y^2=64x$ is tangent to $(x-4{)}^2+(y-2{)}^2=4$ then the possible values of the slope of this chord is

• A. $0,-\frac{12}{35}$
• B. $0,\frac{12}{35}$
• C. $0,\frac{35}{12}$
• D. $0,-\frac{35}{12}$
• E. $0,-\frac{6}{35}$

Answer 1

The correct option is A $0,-\frac{12}{35}$

Focus of parabola is $S(16,0)$
Now equation of tangent to the given circle is given by,
$(y-2)=m(x-4)+2\sqrt{1+m^2}$
Given it is focal chord of the parabola,
$\Rightarrow -2=m\left(12\right)+2\left(\sqrt{1+m^2}\right)\Rightarrow (6m+1{)}^2=(1+m^2)$
$\Rightarrow 35m^2+12m=0\Rightarrow m=0,-\frac{12}{35}$