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Maths-

General

Easy

Question

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

Circle
Parabola
Ellipse
Straight line

The correct answer is: Parabola

$table row cell m subscript o p end subscript cross times m o Q equals 1 end cell row cell fraction numerator 2 over denominator t subscript 1 end subscript end fraction cross times fraction numerator 2 over denominator t subscript 2 end subscript end fraction equals negative 1 rightwards double arrow t subscript 1 end subscript t subscript 2 end subscript equals negative 4 horizontal ellipsis.. left parenthesis 1 right parenthesis end cell row cell text end text text a end text text n end text text d end text text end text h equals fraction numerator a open parentheses t subscript 1 end subscript superscript 2 end superscript plus t subscript 2 end subscript superscript 2 end superscript close parentheses over denominator 2 end fraction end cell row cell equals fraction numerator a open vertical bar open parentheses t subscript 1 end subscript superscript 2 end superscript plus t subscript 2 end subscript superscript 2 end superscript close parentheses minus 2 t subscript 1 end subscript t subscript 2 end subscript close vertical bar over denominator 2 end fraction horizontal ellipsis horizontal ellipsis left parenthesis 2 right parenthesis end cell row cell K equals fraction numerator 2 a open parentheses t subscript 1 end subscript plus t subscript 2 end subscript close parentheses over denominator 2 end fraction rightwards double arrow t subscript 1 end subscript plus t subscript 2 end subscript equals fraction numerator K over denominator a end fraction horizontal ellipsis horizontal ellipsis.. left parenthesis 3 right parenthesis end cell row cell rightwards double arrow text end text text f end text text r end text text o end text text m end text text end text text ( end text text 1 end text text ) end text text , end text text end text text ( end text text 2 end text text ) end text text , end text text end text text ( end text text 3 end text text ) end text text , end text text end text 2 h equals a open square brackets open parentheses fraction numerator K over denominator a end fraction close parentheses to the power of 2 end exponent plus 8 close square brackets end cell row cell rightwards double arrow text end text text P end text text a end text text r end text text a end text text b end text text o end text text l end text text a end text text end text end cell end table$

Related Questions to study

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