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.Maths

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