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 $\left(a , 4 a\right)$ lies on $y^{2}=4ax$

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