Gujarat BoardEnglish MediumSTD 10MathsCo-ordinate Geometry3 Marks
Question
Find a point on $y-$axis which is equidistant form the points $(5, -2)$ and $(-3, 2).$
✓
Answer
The point lies on $y-$axis.
Its $x = 0$
Let the required point be $p(0, y)$ and let $A(5, -2)$ and $B(-3, 2).$
$\therefore PA = PB ⇒ PA^2= PB^2$
$\Rightarrow(5-0)^2+(-2-y)^2=(-3-0)^2+(2-y)^2$
$\text { (By distance formula) }$
$ \Rightarrow 25+4+y^2+4 y=9+4-4 y+y^2 $
$\Rightarrow y^2+4 y+4 y-y^2=13-29 $
$ \Rightarrow 8 y=-16$
$\Rightarrow\ \text{y}=\frac{-16}{8}=-2$
$\therefore$ The reqquired point will be $(0, -2).$
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