S1 : Vertex of a parabola bisects the subtangent.
S2 : Subnormal of a parabola is equal to its latusrectum.
S3 : Circle with focal radius of a point on parabola as diameter touches the tangent drawn at the vertex of the parabola.
S4 : Directrix of a parabola is the tangent of a circle drawn its focal chord as diameter.
Equation of a circle in diametric form -
- wherein
Where are the two diametric ends.
Standard equation of parabola -
- wherein
Equation of tangent -
- wherein
Tangent at
S1 : Tangent at is
This intersect the x-axis and foot of
from A on the x-axis is
clearly origin is the mid point.
S1 is true.
S2 : Equation of normal at is
it intersect x-axis at
subnormal
S2 is False.
S3 : Let be a point on the parabola
.
be the focus equation of circle having AS as diameter is
and tangent at the vertex to the parabola is
. It can be easily checked that
touches this circle.
S3 is true by
S4 : equation of such circle is
Directrix which is tangent.
S4 is true.
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