Questions
The tangent at P, any point on the circle meets the coordinate axes in and then
a
length of AB is constant
b
PA and PB are always equal
c
the locus of the mid-point of AB is x2+y2=x2y2
d
none of these
detailed solution
Correct option is C
Let P(x1,y1) be a point on x2+y2=4. Then, the equation of the tangent at P is xx1+yy1=4This meets the coordinate axes at A4/x1,0 and B0,4/y1. Obviously (a) and (b) are not true. Let (h, k) be the mid-point of AB. Then, h=2x1, k=2y1⇒x1=2h, y1=2kSince, (x1, y1) lies on x2+y2=4∴ 4h2+4k2=4⇒1h2+1k2=1Hence, the locus of (h, k) is 1x2+1y2=1, i.e. x2+y2=x2y2.Talk to our academic expert!
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