Find points on the x – axis, each of which is at a distance of 10 units from the point A(11, – 8).

Question

Philoid · Accepted Answer

Let the point be X(x,0)

XA = 10

By distance formula, as shown below:

XA = √{(11 – x)² + (– 8 – 0)²}

10 = √{(11 – x)² + (– 8)²}

10 = √{121 + x² – 22x + 64}

10 = √{185 + x² – 22x}

Squaring both sides we get

100 = (185 + x² – 22x)

⇒ 85 + x² – 22x = 0

⇒ x² – 22x + 85 = 0

⇒ (x – 5)(x – 17)

⇒ × = 5 or × = 17

The points are (5, 0) and (17, 0)