Find the points on the y-axis, which are at a distance of 13 units each from the point (−5,7).
Let the point on y-axis be B(0,b) and the given point be A(−5,7). The distance between A and B is 13 units.
Now,
AB=13
⇒√{0−(−5)}2+(b−7)2=13 [Using Distance formula: d=√(x2−x1)2+(y2−y1)2]
⇒(0+5)2+(b−7)2=132 [on squaring both sides]
⇒25+b2+49−14b=169
⇒b2−14b−95=0
⇒b2−19b+5b−95=0
⇒b(b−19)+5(b−19)=0
⇒(b−19)(b+5)=0
∴b=19 or −5
Hence, the points are (0,19) and (0,−5).