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The Circle — Maths STD 11 Science — Question

Maharashtra BoardEnglish MediumSTD 11 ScienceMathsThe Circle1 Mark
Question
Write the equation of the circle passing through $(3, 4)$ and touching $y-$axis at the origin.
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Answer

Cirde is touching $y - $axis at the origin.
Thus, centre of cirde is on $x-$ axis.
So Let centre of $d$ rcle is $( h, o)$ Equation of circle is $(x - h)^2 + (y - o)^2 = r^2 ............ (1)$
It is passing through $(3, 4) (3 - h)^2 + (4)^2 = r^2 (3 - h)^2 + 16 = r^2 ............ (2)$
It is also passing through $(3, 4) (0 - h)^2 + (0 - o)^2 = r^2 h^2 = r^2$
Now, equation $( 2)$ be com es, $(3 - h)^2 + 16 = h^2 9 - 6h + h^2 + 16 -6h + 25 = 0$
$\text{h}=\frac{25}{6}$Equation of circle is,
$(x - h)^2 + y^2 = h^2 x^2 - 2xh + y^2 = 0$
$\text{x}^2-2\text{x}\Big(\frac{25}{6}\Big)+\text{y}^2=0$
$6x^2 - 50x + 6y^2 = 0 3x^2 - 25x + 3y^2 = 0 3$
$(x^2 + y^2) - 25x = 0$

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