Q9 of 157 Page 724

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

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)


More from this chapter

All 157 →
7

If the point A(0, 2) is equidistant from the points B(3, p) and C(p, 5), find the value of p. Also, find the length of AB.

 8

Find the point on the x – axis which is equidistant from the points (2, – 5) and (– 2, 9).

 10

Find the point on the y – axis which is equidistant from the points A(6, 5) and B(– 4, 3).

 11

If the point P(x, y) is equidistant from the points A(5, 1) and B(– 1, 5), prove that 3x = 2y.