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Aiswarya Ram Gupta Grade: 12

If the line y=√3X+k touches the circle Xsquare+Ysquare=16, then k=??????

6 years ago

Answers : (3)

vikas askiitian expert
510 Points

x2 + y2 = 16

radius of this circle = a = 4

 line is touches the circle if C = a(1+m2)1/2 ............1

C is y intercept , a is radius of circle , m is slope of line

m = 31/2 , a = 4 , C = k

putting all these values in eq 1

k = 4(1+3)1/2 = 4*2 = 8

6 years ago
PRATIK subramaniyam SAXENA
30 Points

if the line touchs the circle then distance of centre of circle from the line must be the radius of circle.

and the centre of circle is (0,0).

hence distance of the line y=root 3 x +k from (0,0) is 4 units


       ( 0-root3 X 0-k)/root[3+1]  =4

by formula of distance of a point from a line.

on solving it we get k =8

if u like my answer then approve it.

6 years ago
Aiswarya Ram Gupta
35 Points


6 years ago
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