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

= – 1 Ž t₁t₂ = – 4 ....(1)

h = $\frac { \mathrm { a } \left[ \left( \mathrm { t } _ { 1 } + \mathrm { t } _ { 2 } \right) ^ { 2 } - 2 \mathrm { t } _ { 1 } \mathrm { t } _ { 2 } \right] } { 2 }$ …(ii)

$\mathrm { k } = \frac { 2 \mathrm { a } \left( \mathrm { t } _ { 1 } + \mathrm { t } _ { 2 } \right) } { 2 }$ Ž t₁ + t₂ = k/a …(iii)

from (i), (ii) & (iii) 2h =

\ Parabola