If the line 3x-4y=t cuts the circle x^2+y^2-4x-8y-5=0 in two points then limits of t are?
Answer (1)
16th Oct, 2018
steps:
1. first compare the second equation x^2+y^2-4x-8y-5=0 with the eq of center of circle x^2+y^2+2gx+2fy+c=0 , compute the center of the circle that is (-g,-f)
hence here the center of circle is (2,4)
2. calculate the radius : Sqrt(g^2+f^2-c)= 5 units
if the line intersects circle at two points then the length of perpendicular from the center of circle must be less than radius of circle.
|3.2-4.4-t|/(sqrt)(3^2+4^2)< 5
on solving,
|t+10|<25
if |x|<a, then
-a<x<a
= -25<t+10<25
= -25-10<t+10-10<25-10
= -35<t<15
hope you got it.
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