
Find the equations of the circle touching both axes and passing through the point .
Answer
529.2k+ views
Hint: It is given that the circle touches both the and axis. Using this information given in the question, we can draw the figure and we can find the relation between coordinates of the centre of the circle and the radius of the circle.
It is given in the question that the circle is touching i.e. - axis and i.e. - axis and also passing through the point .
Let us assume a circle having it’s centre at the coordinate and it’s radius equal to .
The general equation of this circle is given by .
Since the circle is touching and and also passing through , Using this data, we can now plot the circle.
From the figure drawn above, we can find out that radius of the circle .
and
So, we have a circle with centre and radius
So, from this information, equation of the circle
Cancelling from left side and right side, we get 🡪
Since lies on this circle, we can substitute and in above equation ,
There are two possible values of . So two possible circles corresponding to two possible values of
. Substituting and in equation , the equation of these two circles are
given by 🡪
and
and
Note: There is a possibility of committing a mistake while expanding in equation . There are chances that one may expand it as instead of . This mistake will lead to the incorrect answer.
It is given in the question that the circle is touching
Let us assume a circle having it’s centre at the coordinate
The general equation of this circle is given by
Since the circle is touching
From the figure drawn above, we can find out that radius of the circle
So, we have a circle with centre
So, from this information, equation of the circle
Cancelling
Since
There are two possible values of
given by 🡪
Note: There is a possibility of committing a mistake while expanding
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