Tangents are drawn from the point P(1, 8) to the circle $x^{2} + y^{2} - 6 x - 4 y - 11 = 0$ touch the circle at the point A and B, then equation of the circumcircle of the triangle PAB is

Q. Tangents are drawn from the point

P (3, 4)

to the ellipse

\frac{x^{2}}{9} + \frac{y^{2}}{4} = 1

touching the ellipse at points

A

and

B

The coordinates of

A

and

B

are

Q. From the point A (0, 3) on the circle

x^{2} + 4 x + (y - 3)^{2} = 0

a chord AB is drawn and extended to a point M such that AM =2AB. The equation of the locus of M is___

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Tangents are drawn from the point P(3,4) to the ellipse x29+y24=1 touching the ellipse at points A and B The equation of the locus of the point whose distances from the point P and the line AB are equal is :

The correct option is A 9x2+y2−6xy−54x−62y+241=0Equation of chord of contactx3+y=1Distance from point and line are equal Hence⇒√(x−3)2+(y−4)2=|x+3y−3|√9+110{(x2+9−6x)+(y2+16−8y)}=(x+3y−3)2 →x2+9y2+9+6xy−18y−6x9x2+y2−6xy−54x−62y+241=0

Tangents are drawn from the point $P (3, 4)$ to the ellipse $\frac{x^{2}}{9} + \frac{y^{2}}{4} = 1$ touching the ellipse at points $A$ and $B$ The equation of the locus of the point whose distances from the point $P$ and the line $A B$ are equal is :