Question

The circles described on a focal length(of a parabola) as diameter always touches

• A. The tangent at the vertex
• B. The axis
• C. The directrix
• D. Latus rectum

Answer 1

The correct option is A The tangent at the vertex

The circle on $SP$ as diameter is
$(x-a{t}_1^2)(x-a)+(y-2a{t}_1)y=0\Rightarrow x^2+y^2-ax(t_1^2+1)-2ay{t}_1+a^2{t}_1^2=0$


The $y$ intercept of the circle is
$2\sqrt{f^2-c}=\sqrt{a^2{t}_1^2-a^2{t}_1^2}=0$

As $y-$intercept made by the circle is $0$, so $y-$axis is a tangent at the vertex.