HARD
JEE Advanced
IMPORTANT
Earn 100

Find the locus of a point whose distance from a fixed point is in a constant ratio (not equal to 1) to the length of the tangent drawn from it to a given circle.

Important Questions on The Circle

HARD
JEE Advanced
IMPORTANT
The Elements of COORDINATE GEOMETRY Part 1 Cartesian Coordinates>Chapter 6 - The Circle>EXAMPLES XXII>Q 6
Find the locus of the vertex of a triangle, given 1 its base, and the sum of the squares of its sides, 2 its base and the sum of m times the square of one side and n times the square of the other.
EASY
JEE Advanced
IMPORTANT
The Elements of COORDINATE GEOMETRY Part 1 Cartesian Coordinates>Chapter 6 - The Circle>EXAMPLES XXII>Q 7
A point moves so that the sum of the squares of its distances from n fixed points is given. Prove that its locus is a circle.
EASY
JEE Advanced
IMPORTANT
The Elements of COORDINATE GEOMETRY Part 1 Cartesian Coordinates>Chapter 6 - The Circle>EXAMPLES XXII>Q 8
Whatever be the value of α, prove that the locus of the intersection of the straight lines, xcosα+ysinα=a and xsinα-ycosα=b is a circle.
HARD
JEE Advanced
IMPORTANT
The Elements of COORDINATE GEOMETRY Part 1 Cartesian Coordinates>Chapter 6 - The Circle>EXAMPLES XXII>Q 9
From a point P on a circle, perpendiculars PM and PN are drawn to two radii of the circle which are not at right angles; find the locus of the middle point of MN.
HARD
JEE Advanced
IMPORTANT
The Elements of COORDINATE GEOMETRY Part 1 Cartesian Coordinates>Chapter 6 - The Circle>EXAMPLES XXII>Q 10
Tangents are drawn to a circle from a point that always lies on a given line. Prove that the locus of the middle point of the chord of contact is another circle.
EASY
JEE Advanced
IMPORTANT
The Elements of COORDINATE GEOMETRY Part 1 Cartesian Coordinates>Chapter 6 - The Circle>EXAMPLES XXII>Q 11
Find the locus of the middle point of chord of circle x2+y2=a2 which passes through the points (h, k).
HARD
JEE Advanced
IMPORTANT
The Elements of COORDINATE GEOMETRY Part 1 Cartesian Coordinates>Chapter 6 - The Circle>EXAMPLES XXII>Q 12
Find the locus of the middle points of chords of the circle x2+y2=a2 which subtend a right angle at the point c,0.
HARD
JEE Advanced
IMPORTANT
The Elements of COORDINATE GEOMETRY Part 1 Cartesian Coordinates>Chapter 6 - The Circle>EXAMPLES XXII>Q 13
O is a fixed point and, P is any point on a fixed circle. A point, Q is taken, on OP such that, OQ is in a constant ratio to OP. Prove that the locus of Q is a circle.