The Harmonic conjugate of (4,-2) with respect to the points(2, -4) and (7, 1) is - Maths -

Question

The Harmonic conjugate of (4,-2) with respect to the points(2, -4)
and (7, 1) is

Brijendra P. · Accepted Answer

<img alt="" src=
"https://s3mn%20mnimgs%20com/img/shared/content_ck_images/images/TTTTTTTTTTTTTTTTTTTTTTTTT%20png"
style="width: 765px; height: 312px;">
Now using first condition, ACCB=-ADDB2-42+-4+224-72+-2-12=-x-22+y+42x-72+y-122232=-x-22+y+42x-72+y-124x-72+y-12=9x-22+y+424x2-56x+196+4y2+4-8y=9x2-36x+36+9y2+144-72y5x2+20x+36+5y2-64y-20=0
1Now mid point of AB is O = 2+72, -4+12=O92,-32Now using second condition, OB2=OC×OD92-72+-32-12=92-42+-32+22×92-x2+-32-y2Squaring we get, 92-72+-32-12=92-42+-32+22×92-x2+-32-y2Now simplify the above equation  for your own practice to get a equation in x and y and then solve it with the equation 1 to getthe value of x and y

The Harmonic conjugate of (4,-2) with respect to the points(2, -4) and (7, 1) is...