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Given family of lines a(3x+4y+6)+b(x+y+2)=0.the line of the family situated at the greatest distance from the point P(2,3) has the equation?

Given family of lines a(3x+4y+6)+b(x+y+2)=0.the line of the family situated at the greatest distance from the point P(2,3) has the equation?

Grade:12

1 Answers

Joanna
11 Points
4 years ago
Find the common point of intersection of this family of lines. Here it is (-2,0). Now, given point is (2,3). Equation of line passing through both the points is : 3x + 6 =4y. You actually only need the slope of this line which is : 3/4 Line perpendicular to this line passing through the common point will be at the greatest distance. Slope of the required line: -4/3Equation of the line :-4/3{x-(-2)} = y-0After solving, equation is : 4x + 3y + 8 =0.

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