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Find the equation to the tangent with the circle x 2 + y 2 = a 2 which is parallel to the straight line y = mx + c

Find the equation to the tangent with the circle x2 + y2 = a2 which is parallel to the straight line y = mx + c

Grade:10

1 Answers

Aditya Gupta
2081 Points
3 years ago
hello samaira, thanks 4 d ques.
note that any line parallel to y = mx + c will have the slope m.
lets call it L: y= mx + p
we know that any tangent line to a circle touches the circle at 1 point and is thus at a radial distance from the centre of the circle.
we know the formula of finding the distance of a point from a line.
also, x2 + y2 = a2 has radius of a units and centre is at (0, 0).
so, a= |m*0 + p – 0|/sqrt(1+m^2)
or |p|= a*sqrt(1+m^2)
or p= ± a*sqrt(1+m^2)
so, there are 2 such parallel lines:
y= mx ± a*sqrt(1+m^2)
kindly approve ;)

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