Question

The triangle formed by the tangents by the tangents to a parabola $y^2=4ax$ at the ends of the rectum is

• A. equilateral
• B. isosceles
• C. right-angled isosceles
• D. dependent on the value of a for its classification

Answer 1

The correct option is C right-angled isosceles

The triangle formed by the tangent to a parabola at the ends of rectum is to be found

Let BC is rectum

AB=AC

Equation of tangent to parabola $y^2=4ax$ at $(a,2a)$ is

$2ay=2a(x+a)y=x+aA(y=0)x=-aA\equiv (-a,0)$

Angle between $BAS=\frac{\pi }{4}$

Angle between $CAS=\frac{\pi }{4}$

Hence angle $BAC=\frac{\pi }{2}$

Therefore triangle formed is a right angled isosceles .