Locus

Q. 62. Find the equation of locus of a point which moves such that its distance from the Axis of X is there times the distance from the axis of Y .

Q. A variable chord of circle $x^2+y^2=4$ is drawn from the point $P(3,5)$ meeting the circle at the points $A$ and
$B$. A point $Q$ is taken on this chord such that $2PQ=PA+PB$. Locus of ${}^{\prime \prime }{Q}^{\prime \prime }$ is

1. $x^2+y^2+3x+4y=0$
2. $x^2+y^2=36$
3. $x^2+y^2=16$
4. $x^2+y^2-3x-5y=0$

Q. A man running a racecourse notes that the sum of the distances from the two flag posts form him is always 10 m and the distance between the flag posts is 8 m. find the equation of the posts traced by the man.

Q. If a variable tangent of the circle $x^2+y^2=1$ intersect the ellipse $x^2+2y^2=4$ at P and Q then the locus of the points of intersection of the tangents at P and Q is

1. A circle of radius 2 units
2. A parabola with fouc as (2, 3)
3. An ellipse with eccentricity $\frac{\sqrt{3}}{4}$
4. An ellipse with length of latus rectrum is 2 units

Q. If tangents are drawn to the ellipse $x^2+2y^2=2$ at all points on the ellipse other than its four vertices, then the mid points of the tangents intercepted between the coordinates axes lie on the curve :

1. $\frac{1}{2x^2}+\frac{1}{4y^2}=1$
2. $\frac{1}{4x^2}+\frac{1}{2y^2}=1$
3. $\frac{x^2}{2}+\frac{y^2}{4}=1$
4. $\frac{x^2}{4}+\frac{y^2}{2}=1$

Q. A variable circle passes through the point $P(1,2)$ and touches the $x-$axis. The locus of the other end of the diameter through $P$ is

1. $(x-1{)}^2=8y$
2. $(x+1{)}^2=8y$
3. $(y-1{)}^2=8x$
4. $(x-1{)}^2+8y=0$