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

Question

Aditya Gupta · Answer

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, x 2 + y 2 = a 2 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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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

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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

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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