Question bank/JEE Main/Mathematics
JEE MainMathematics
A circle is drawn to pass through the extremities of the latus
rectum of the parabola y2 = 20x. It is given that this circle also
touches the directrix of the parabola. Radius of this circle is equal to
Show answer and solution
Extrimities of the latus rectum are (5, 10) and (5, - 10)
Since any circle drawn with any focal chord as its diameter touches the
directrix, thus the equation of the required circle is
(x - 5)2 + (y - 10)(y + 10) = 0
[IMAGE] (circle touching the directrix at (-5, 0)
which is the foot of the directrix)
i.e. x2 + y2 - 10x - 75 = 0
its radius = 10
Since any circle drawn with any focal chord as its diameter touches the
directrix, thus the equation of the required circle is
(x - 5)2 + (y - 10)(y + 10) = 0
[IMAGE] (circle touching the directrix at (-5, 0)
which is the foot of the directrix)
i.e. x2 + y2 - 10x - 75 = 0
its radius = 10
Source: Grass-G / M-01 Mathematics Paper-1.docx
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