Question

If $y=m_{1}x+c$ and $y=m_{2}x+c$ are two tangents to the parabola $y^2+4a(x+a)=0$, then

• A. $m_1+m_2=0$
• B. $1+m_1+m_2=0$
• C. $m_1{m}_2-1=0$
• D. $1+m_1{m}_2=0$

Answer 1

The correct option is D $1+m_1{m}_2=0$

Given equation of parabola is
$y^2+4a(x+a)=0$
$\Rightarrow y^2=-4a(x+a)$
Vertex of parabola is shifted $a$ units to the right.
Equation of directrix is $x=0$ i.e. $y-$axis.
Equation of tangents are
$y=m_{1}x+c$
$y=m_{2}x+c$
Since these tangents intersect at $(0,c)$ which lies on directrix.
Hence tangents are perpendicular.
$\Rightarrow m_1{m}_2=-1$
or, $m_1{m}_2+1=0$