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. Circle
• B. Parabola
• C. Ellipse
• D. Straight line

Answer 1

Answer: (B)

Parabola

Answer 2

m_op × m_OQ = 1

$\frac{2}{t_{1}} \times \frac{2}{t_{2}}$ = –1 ̃ t₁t₂ = –4 .....(1)

and h = $\frac{a(t_{1}^{2} + t_{2}^{2})}{2}$

= $\frac{a|(t_{1}^{2} + t_{2}^{2}) - 2t_{1}t_{2}|}{2}$ ......(2)

K = $\frac{2a(t_{1} + t_{2})}{2}$ ̃ t₁ + t₂ = $\frac{K}{a}$ .......(3)

̃ from (1), (2), (3), 2h = $a\left\lbrack \left( \frac{K}{a} \right)^{2} + 8 \right\rbrack$

̃ Parabola