Question

The locus of the middle point of chords of parabola which subtends 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)

h = $\frac{a(t_{1}^{2} + t_{2}^{2})}{2}$=$\frac{a\lbrack(t_{1} + t_{2})^{2}–2t_{1}t_{2}\rbrack}{2}$ …(ii)

$k = \frac{2a(t_{1} + t_{2})}{2}$ ̃ t₁ + t₂ = k/a …(iii)

from (i), (ii) & (iii) 2h = $a\left\lbrack \left( \frac{k}{a} \right)^{2} + 8 \right\rbrack$

\ Parabola