10th Class Mathematics Coordinate Geometry Question Bank MCQs - Coordinate Geometry

The coordinate of a point on Y-axis which is equidistant from the point \[A\left( 6,\,5 \right)\]and\[B\left( -4,\,3 \right)\], will be

A) (0, 9)

B) (0, -9)

C) (0, 5)

D) (0, 3)

Correct Answer: A

Solution :

Let point on F-axis be P(0, k).

Then, \[P{{A}^{2}}=P{{B}^{2}}\]

\[\Rightarrow \,\,\,{{\left( 6-0 \right)}^{2}}+{{\left( 5-k \right)}^{2}}={{\left( -4-0 \right)}^{2}}+{{\left( 3-k \right)}^{2}}\]

\[\Rightarrow \,\,\,36+25+{{k}^{2}}-10k=16+9+{{k}^{2}}-6k\]

\[\Rightarrow \,\,\,4k=36\,\,\Rightarrow k=9\]

Hence, coordinates of point on Y-axis are (0,9).