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Question

Find the equation of the circle which touches the y-axis at a distance of 4 units from the origin and cuts an intercept of 6 units from the axis of x.


Solution

Consider the diagram shown below.

 

The circle touches y-axis at $$\left( 0,4 \right)$$. SO, the centre will lie on $$y=4$$. Therefore, y-coordinate of the circle will be $$4$$.

 

Now,

$$ CD=6 $$

$$ \Rightarrow CM=3 $$

 Again,

$$RM=4$$

 

Using Pythagoras theorem, we have

$$CR=\sqrt{{{3}^{2}}+{{4}^{2}}}=5$$ $$=$$ Radius of the circle

 

Therefore,

Centre of the circle, $$R=\left( 5,4 \right)$$

 

Therefore, required equation of the circle is,

$$ {{\left( x-5 \right)}^{2}}+{{\left( y-4 \right)}^{2}}={{5}^{2}} $$

$$ {{x}^{2}}+{{y}^{2}}-10x-8y+16=0 $$


Hence, this is the required result.


1003606_1069688_ans_97dbccc00449400d8d7792f13a56fd62.png

Maths

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