From the point A(0.3) on the circle x2+4 x+(y-3)2=0 a chord A B is drawn extended to a point M such that A M=2 A B. The equation of the locus of M is :

Question

From the point A(0.3) on the circle x2+4 x+(y-3)2=0 a chord A B is drawn extended to a point M such that A M=2 A B. The equation of the locus of M is : (A) x2+8 x+y2=0 (B)  x2+8 x+(y-3)2=0 (C) (x-3)2+8 x+y2=0 (D) x2+8 x+8 y2=0

Tardigrade Admin · Accepted Answer

<img class="img-fluid question-image" alt="image" src="https://cdn.tardigrade.in/img/question/mathematics/d7d57cc042b2f3e2788b5444940f46d5-.png" /> B lies on circle (( h /2))2+4(( h /2))+(( k +3/2)-3)2=0 ⇒ ( h 2/4)+2 h +(( k -3)2/4)=0 Hence locus of (h, k) x2+8 x+(y-3)2=0

Q. From the point $A (0.3)$ on the circle $x^{2} + 4 x + (y - 3)^{2} = 0$ a chord $A B$ is drawn \& extended to a point $M$ such that $A M = 2 A B$ . The equation of the locus of $M$ is :

$x^{2} + 8 x + y^{2} = 0$

$x^{2} + 8 x + (y - 3)^{2} = 0$

$(x - 3)^{2} + 8 x + y^{2} = 0$

$x^{2} + 8 x + 8 y^{2} = 0$

B lies on circle
$(\frac{h}{2})^{2} + 4 (\frac{h}{2}) + (\frac{k + 3}{2} - 3)^{2} = 0$
$\Rightarrow \frac{h ^{2}}{4} + 2 h + \frac{( k - 3 ) ^{2}}{4} = 0$
Hence locus of $(h, k) x^{2} + 8 x + (y - 3)^{2} = 0$

Q. From the point A(0.3) on the circle x2+4x+(y−3)2=0 a chord AB is drawn \& extended to a point M such that AM=2AB. The equation of the locus of M is :

x2+8x+y2=0

x2+8x+(y−3)2=0

(x−3)2+8x+y2=0

x2+8x+8y2=0