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Question

Let the line 2x+3y=18 meet the circle x2+y2=25 at P (α,β) where α,β  N.  Let Q (β,α) be another point on the above circle.  Then


A
PQ=52
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B
PQ=25
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C
Tangent at P is perpendicular to the tangent at Q.
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D
Tangent at P is parallel to the tangent at Q.
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Solution

The correct options are
A PQ=52
C Tangent at P is perpendicular to the tangent at Q.
2x+3y=18y=182x3
(182x3)2=25x2=3,3313
But α,βN,     x=3y=4
P=(3,4),        Q=(4,3)
(a) PQ=50=52
(b) x2+y2=25dydx=xy
Slope of tangent at P,m1=34
at Q,m2=43
m1m2=1 perpendicular

Mathematics

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