The locus of a point which moves such that the tangents from it to the two circles $$x2+y2$$−$$5x$$−$$3=0$$ and $$3x2+3y2+2x+4y$$−$$6=0$$ are equal, is given by

Question

The locus of a point which moves such that the tangents from it to the two circles $$x2+y2$$−$$5x$$−$$3=0$$ and $$3x2+3y2+2x+4y$$−$$6=0$$ are equal, is given by

Infinity Learn · Accepted Answer

Let P (h$$, $$k) be the coordinates of a point from which equal tangents are drawn to the circles $$x2+y2$$−$$5x$$−$$3=0$$  and $$3x2+3y2+2x+4y$$−$$6=0$$. Then,$$h2+k2$$−$$5h$$−$$3=h2+k2+23h+43k$$−$$2$$⇒ $$17h+4+3=0Hence$$, the locus of (h$$, $$k) is $$17x+4y+3=0ALITER$$ Required locus is the radical axis of the given circles and its equation is given by $$S1$$−$$S2=0$$⇒$$x2+y2$$−$$5x$$−$$3$$−$$x2+y2+23x+43y$$−$$2=0$$⇒$$17x+4y+3=0$$

The locus of a point which moves such that the tangents from it to the two circles $x^{2} + y^{2} - 5 x - 3 = 0$ and $3 x^{2} + 3 y^{2} + 2 x + 4 y - 6 = 0$ are equal, is given by

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The locus of a point which moves such that the tangents from it to the two circles x2+y2−5x−3=0 and 3x2+3y2+2x+4y−6=0 are equal, is given by

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The locus of a point which moves such that the tangents from it to the two circles $x^{2} + y^{2} - 5 x - 3 = 0$ and $3 x^{2} + 3 y^{2} + 2 x + 4 y - 6 = 0$ are equal, is given by