Question

If $y+b=m_1(x+a),y+b=m_2(x+a)$ are two tangents to the parabola $y^2=4ax,$ then

• A. $m_1\cdot m_2=-1$
• B. $m_1\cdot m_2=1$
• C. $m_1+m_2=0$
• D. $m_1-m_2=0$

Answer 1

The correct option is A $m_1\cdot m_2=-1$

$y+b=m_1(x+a)y+b=m_2(x+a)$
These two tangents are drawn from point $(-a,-b)$
Clearly $(-a,-b)$ lies on $x=-a$ line, which is directrix of $y^2=4ax$
$\therefore$ tangents have to be perpendicular
$m_1\cdot m_2=-1$