If 5x - 12y + 10 = 0 and 12y - 5x + 16 = 0 ar | vedclass

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(A) The given equations of the tangents are $5x - 12y + 10 = 0$ and $12y - 5x + 16 = 0$.Rewriting the second equation to match the form $ax + by + c =

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(A) The given equations of the tangents are $5x - 12y + 10 = 0$ and $12y - 5x + 16 = 0$.Rewriting the second equation to match the form $ax + by + c = 0$,we get $5x - 12y - 16 = 0$.Since the tangents are parallel,the distance between them is the diameter of the circle.The distance $d$ between two parallel lines $ax + by + c_1 = 0$ and $ax + by + c_2 = 0$ is given by $d = \frac{|c_1 - c_2|}{\sqrt{a^2 + b^2}}$.Here,$a = 5$,$b = -12$,$c_1 = 10$,and $c_2 = -16$.$d = \frac{|10 - (-16)|}{\sqrt{5^2 + (-12)^2}} = \frac{|26|}{\sqrt{25 + 144}} = \frac{26}{\sqrt{169}} = \frac{26}{13} = 2$.Since the diameter $d = 2$,the radius $r = \frac{d}{2} = \frac{2}{2} = 1$.

If $5x - 12y + 10 = 0$ and $12y - 5x + 16 = 0$ are two tangents to a circle,then the radius of the circle is

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