Question

find the points on y-axis which are at distance of 13 units from the point (12,-3)

Answer 1

it is (0,-8) and (0,2)

Answer 2

The points on y-axis which are at distance of 13 units from the point (12,-3) are (0, 2) and (0, -8)

Given:

The points on y-axis is at distance of 13 units from the point (12, -3)

To find:

The points which are at distance of 13 units from (12, -3)

Solution:

Let the required point on y-axis is  P(0, y) and A be the point (12, -3)

From given data distance the distance between P and A = 13 units

As we know distance between 2 points = $\sqrt{(x_{2}-x_{1}) ^{2} +(y_{2} -y_{1} )^{2} }$  

⇒ distance between P(0, y)  and  A(12, -3)

PA = $\sqrt{(0-12) ^{2} +(y +3 )^{2} }$  

From given data

$\sqrt{(0-12) ^{2} +(y +3 )^{2} } = 13$    

$(0-12) ^{2} +(y +3 )^{2} = 169$    [ do squaring on both sides  ]

⇒ 144 + y² + 9 + 6y = 169  

⇒  y² + 6y = 16        [ factorise the equation ]

⇒  y² + 6y - 16 = 0

⇒  y² - 2y + 8y - 16 = 0  

⇒ y (y - 2) + 8(y-2) = 0

⇒ (y - 2) (y + 8) = 0

⇒ y - 2 = 0 ⇒ y = 2

⇒ y + 8 = 0 ⇒ y = -8

Therefore, the points on y-axis are (0, 2) and (0, -8)

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