Locus
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Q. Let RS be the diameter of the circle x2+y2=1, where S is the point (1, 0). Let P be a variable point (other than R and S) on the circle and tangents to the circle at S and P meet at the point Q. The normal to the circle at P intersects a line drawn through Q parallel to RS at point E. Then the locus of E passes through the point(s).
- (13, −1√3)
- (13, 1√3)
- (14, −12)
- (14, 12)
Q.
A ladder starts sliding on a wall from its initial position (fig 1) and (fig 2) is an intermediate stage
before it completely hits the ground. Find the locus of the curve traced by the mid-point of the ladder.
(a and b are constants).
Q.
A ladder starts sliding on a wall from its initial position (fig 1) and (fig 2) is an intermediate stage
before it completely hits the ground. Find the locus of the curve traced by the mid-point of the ladder.
(a and b are constants).
Q. A variable chord of circle x2+y2=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 ′′Q′′ is
B. A point Q is taken on this chord such that 2PQ=PA+PB. Locus of ′′Q′′ is
- x2+y2+3x+4y=0
- x2+y2=16
- x2+y2=36
- x2+y2−3x−5y=0
Q. Let RS be the diameter of the circle x2+y2=1, where S is the point (1, 0). Let P be a variable point (other than R and S) on the circle and tangents to the circle at S and P meet at the point Q. The normal to the circle at P intersects a line drawn through Q parallel to RS at point E. Then the locus of E passes through the point(s).
- (13, 1√3)
- (14, 12)
- (13, −1√3)
- (14, −12)
Q. Locus of the centre of the circle which always passes through the fixed point (a, 0) and (−a, 0), where a≠0, is
- x=1
- x+y=2a
- x+y=6
- x=0
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
- (x−1)2=8y
- (y−1)2=8x
- (x−1)2+8y=0
- (x+1)2=8y
Q. The circle x2+y2−4x−4y+4=0 is inscribed in a triangle which has two of its sides along the coordinate axes. If the locus of the circumcentre of the triangle is x+y−xy+k√x2+y2=0, then the value of k is equal to
- 2
- 3
- −2
- 1
Q. If a variable tangent of the circle x2+y2=1 intersect the ellipse x2+2y2=4 at P and Q then the locus of the points of intersection of the tangents at P and Q is
- A circle of radius 2 units
- A parabola with fouc as (2, 3)
- An ellipse with eccentricity
- An ellipse with length of latus rectrum is 2 units
Q. If one axis of varying standard hyperbola be fixed in magnitude and position, then the locus of the point of contact of tangents drawn to it from a fixed point (0, c) on the other axis is
- y2=a2c(x−c)
- x2=−a2c(y−c)
- x2=a2c(y+c)
- y2=−a2c(x−c)