Question

If a double ordinate of the parabola $y^2=4ax$ is of length $8a$ , then the triangle formed by double ordinate and line joining vertex with end points of double ordinate is a

• A. equilateral triangle
• B. obtuse angled triangle
• C. right angled triangle
• D. None of these

Answer 1

Answer: (C)

Here, the given parabola $y^2=4ax$ , then $\left(a,4a\right)$ lies on $y^2=4ax$

$\Rightarrow 16a^2=4a\alpha$
$\Rightarrow \alpha =4a$
Slope of $OA=\frac{4a-0}{4a-0}=1=m_1$
Slope of $O{A}^{\prime }=\frac{-4a-0}{4a-0}=-1=m_2$
$m_1{m}_2=-1,OA\perp O{A}^{\prime }$
Hence, $△OA{A}^{\prime }$ is a right angled triangle.