JEE Main 2019 — Circle Question with Solution
From: JEE Main 2019 (Online) 9th April Morning Slot
Question
If a tangent to the circle x2 + y2 = 1 intersects
the coordinate axes at distinct points P and Q,
then the locus of the mid-point of PQ is :
Choose an option
Show full solutionCorrect option: A
Correct answer
Ax2 + y2 – 4x2y2 = 0
Step-by-step explanation
Equation of tangent at A,
xcos + ysin = 1
P(sec, 0) and Q(0, cosec)
Let M(h, k) is the mid-point of PQ.
h =
2h = sec
cos = .....(1)
k =
2k = cosec
sin = .....(2)
From (1) and (2),
sin2 + cos2 =
Locus of the midpoint,
x2 + y2 – 4x2y2 = 0
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