Question #60f1a Geometry Angles and Intersecting Lines Angles Between Intersecting and Parallel Lines 1 Answer Alberto P. Nov 3, 2016 P_(1,2)=(a+-a/bsqrt(a^2+b^2);0) Explanation: Let P=(x_0;0) on the x axis x/a+y/b=1\ \ \ is equivalent to bx+ay-ab = 0 The distance of the generic P to this line is abs(bx_0+a0-ab)/sqrt(a^2+b^2)\ \ \ and must be =a so abs(bx_0-ab)=asqrt(a^2+b^2) (bx_0-ab)^2=a^2(a^2+b^2) b^2x_0^2+a^2b^2-2ab^2x_0=a^2(a^2+b^2) b^2x_0^2-2ab^2x_0 +a^2b^2-a^4-a^2b^2 =0 x_(1,2)=(ab^2+-sqrt(a^2b^4+a^4b^2))/b^2=a+-a/bsqrt(a^2+b^2) Answer link Related questions When given line y=2x + 3 and point (4,2), how would you find a parallel and a perpendicular line? What is the relationship between two perpendicular lines? What are some examples? Consider the line y=8x-2. What is the equation of the line that is parallel to this line and... What is the equation of the line that is perpendicular to the line 3x + y = 7 and passes... What is the equation of a line that satisfies the given conditions: perpendicular to #y= -2x +... What is the equation of a line that satisfies the given conditions: perpendicular to #y= -2x +... What line is perpendicular to y = -3 and passes through point (4, -6)? Perpendicular lines have _________ slopes? What is an equation of the line that has a y-intercept of -2 and is perpendicular to the line... What is the equation of the line in slope-intercept that is perpendicular to the line #4y - 2 =... See all questions in Angles Between Intersecting and Parallel Lines Impact of this question 2349 views around the world You can reuse this answer Creative Commons License