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