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Question

px+qy=40 is a chord of minimum length of the circle (x10)2+(y20)2=729. If the chord passes through (5,15), then p2019+q2019 is equal to


Your Answer
A
0
Your Answer
B
2
Your Answer
C
22019
Correct Answer
D
22020

Solution

The correct option is D 22020
Given, equation of circle
(x10)2+(y20)2=729
Centre (C)(10,20) and radius =729=27


Equation of chord : px+qy=40
Slope of chord =pq

Since, chord is of minimum length.
P(5,15) will be the mid point of given chord.
We know that, any chord and the straight line passing through its midpoint and centre of the circle are perpendicular to each other.
mCP×mchord=12015105×pq=1p=q

Also, chord passes through (5,15).
5p+15p=40
p=q=2

p2019+q2019=22020

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