Last Updated On [03-11-2023]
The locus of the mid-points of the portion of the normal to the parabola 
intercepted between the curve and the axis is another parabola whose latus rectum is
The locus of the mid-points of the portion of the normal to the parabola intercepted between the curve and the axis is another parabola whose latus rectum is
Question ID - 153535 :-
The locus of the mid-points of the portion of the normal to the parabola intercepted between the curve and the axis is another parabola whose latus rectum is
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The locus of the mid-points of the portion of the normal to the parabola |
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Consider the parabola 
We have to find the locus of 
, since 
has ordinate 
, ordinate of 
is 
Also 
is on the curve, then abscissa of 
is 
Now 
is normal to curve
Slope of tangent to curve at any point 
Hence slope of normal at point 
is
Also slope of normal joining 
and 
is 
Hence comparing slopes 
or 
For 
hence locus us
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