If the tangents are drawn to the $$circlex2+y2=12$$ at the point where it meets the circle $$x2+y2$$−$$5x+3y$$−$$2=0$$ then the point of intersection of these tangents, is

Question

If the tangents are drawn to the $$circlex2+y2=12$$ at the point where it meets the circle $$x2+y2$$−$$5x+3y$$−$$2=0$$ then the point of intersection of these tangents, is

Infinity Learn · Accepted Answer

Let (h$$, $$k) be the point of intersection of the tangents. Then, the chord of contact of tangents is the common chord of the circles $$x2+y2=12$$ and $$x2+y2$$−$$5x+3y$$−$$2=0The$$ equation of the common chord is $$5x$$−$$3y$$−$$10=0Also$$, the equation of the chord of contact $$ishx+ky$$−$$12=0Equations$$ (i) and (ii) represent the same line. Therefore, $$h5=k$$−$$3=$$−$$12$$−$$10$$⇒$$h=6$$,$$k=$$−$$18/5Hence$$, the required point is (6$$,−$$18/5).

If the tangents are drawn to the circle $x^{2} + y^{2} = 12$ at the point where it meets the circle $x^{2} + y^{2} - 5 x + 3 y - 2 = 0$ then the point of intersection of these tangents, is

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If the tangents are drawn to the circlex2+y2=12 at the point where it meets the circle x2+y2−5x+3y−2=0 then the point of intersection of these tangents, is

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If the tangents are drawn to the circle $x^{2} + y^{2} = 12$ at the point where it meets the circle $x^{2} + y^{2} - 5 x + 3 y - 2 = 0$ then the point of intersection of these tangents, is