If the lines 3x-4y+4=0 and 6x-8y-7=0 are the tangents to a circle, then find the radius of the circle.
Answers
Answer:
Radius = 3/4
Step-by-step explanation:
As 3/4 = 6/8 (the coefficients of x and y), the lines are parallel. So they are tangents at either end of a diameter. To get the radius, we just need the distance between these parallel lines, and then halve it.
The directed distance from the origin to the line 3x-4y+4=0 is
4/√(3²+4²) = 4/5
The distance from the origin to the line 6x-8y-7=0 is
-7/√(6²+8²) = -7/10
The distance between the lines is therefore
4/5 - (-7/10) = 8/10 + 7/10 = 15/10 = 3/2.
The radius of the circle is therefore
(3/2) / 2 = 3/4
Answer:
As 3/4 = 6/8 (the coefficients of x and y), the lines are parallel. So they are tangents at either end of a diameter. To get the radius, we just need the distance between these parallel lines, and then halve it.
The directed distance from the origin to the line 3x-4y+4=0 is
4/√(3²+4²) = 4/5
The distance from the origin to the line 6x-8y-7=0 is
-7/√(6²+8²) = -7/10
The distance between the lines is therefore
4/5 - (-7/10) = 8/10 + 7/10 = 15/10 = 3/2.
The radius of the circle is therefore
(3/2) / 2 = 3/4
Step-by-step explanation: