Question

Obtain the equation of the lines passing through the foot of the perpendicular from (h,k) on the line Ax + By + C =0 and bisecting the angle between the perpendicular and the given line​

Answer 1

Answer:

Ax+By+C=0.......(i)

Slope of line =m=−

B

A

Let the slope of perpendicular be m

′

mm

′

=−1

−

B

A

m

′

=−1

⇒m

′

=

A

B

Equation of perpendicular is

y−k=

A

B

(x−h)

Ay−Ak=Bx−Bh

Bx−Ay+Ak−Bh=0......(ii)

Angle bisector of (i) and (ii) is

B

2

+A

2

Bx−Ay+Ak−Bh

=±

A

2

+B

2

Ax+By+C

Bx−Ay+Ak−Bh=±(Ax+By+C)

B(x−h)−A(y−k)=±(Ax+By+C)