Question

The locus of the middle points of chords of a parabola which subtend a right angle at the vertex of the parabola, is –

• A. A circle
• B. An ellipse
• C. A parabola
• D. A hyperbola

Answer 1

Answer: (C)

A parabola

Answer 2

Let y² = 4ax ..... (i)

PM = QM \end{matrix}$$ M$\left\{ \begin{aligned} & h = \frac{at_{1}^{2} + at_{2}^{2}}{2} .....(ii) \\ & k = 2a\frac{(t_{1} + t_{2})}{2} .....(iii) \end{aligned} \right.\ $ & if PQ subtends the right angle at the vertex of the parabola, then $\begin{matrix} t_{1}t_{2} = –4 \end{matrix}$ ..... (iv) By (ii), (iii) & (iv) Ž eliminate t₁ & t₂