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JEE Main & Advanced Sample Paper JEE Main Sample Paper-1

  • question_answer
    Area of the triangle formed by the tangents and chord of contact of the   circle \[{{x}^{2}}+{{y}^{2}}+6x+8y=0\], if tangents, are drawn from the point (1, 1), is

    A)  \[\frac{340}{41}\]sq unit             

    B)   \[\frac{360}{41}\]sq unit

    C)  \[\frac{320}{41}\]sq unit             

    D)  None of these

    Correct Answer: C

    Solution :

    Equation of given circle is \[{{x}^{2}}+{{y}^{2}}+6x+8y=0\]                                                ?(i) At point (1,1), \[{{S}_{1}}={{1}^{2}}+{{1}^{2}}+6+8\] \[=1+1+6+8=16\] Now, radius r \[r=\sqrt{{{3}^{2}}+{{4}^{2}}}=5\] Area of required triangle \[=\frac{rS_{1}^{3/2}}{{{r}^{2}}+{{S}_{1}}}\] \[=\frac{5\times {{16}^{3/2}}}{{{5}^{2}}+16}\]                    \[=\frac{320}{41}\]sq unit


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