MEDIUM
JEE Main
IMPORTANT
Earn 100

If P and Q be a pair of conjugate points with respect to a circle S. Prove that the circle on PQ as diameter cuts the circle S orthogonally.

Important Questions on Circle

HARD
JEE Main
IMPORTANT

Two circles are drawn through the points (a, 5a) and (4a, a) to touch the axis of y, where a>0. Prove that they intersect at an angle tan-1409.

EASY
JEE Main
IMPORTANT

Find the condition that the chord of contact of tangents from the point α,β to the circle x2+y2=a2 should subtend a right angle at the centre. Hence find the locus of α,β.

EASY
JEE Main
IMPORTANT
Find the locus of the middle point of chord of circle x2+y2=a2 which passes through the points (h, k).
HARD
JEE Main
IMPORTANT
Show that the locus of the point the tangents from which to the circle x2+y2-a2=0 include a constant angle α is x2+y2-2a22tan2α=4a2x2+y2-a2.
MEDIUM
JEE Main
IMPORTANT
O is a fixed point and AP and BQ are two fixed parallel straight lines. BOA is perpendicular to both and  POQ is a right angle. Prove that the locus of the foot of the perpendicular drawn from O upon PQ is the circle with AB as a diameter.
EASY
JEE Main
IMPORTANT
The tangent at any point P on the circle x2+y2=2 cuts the axes in L and M. Find the locus of the middle point of LM.
HARD
JEE Main
IMPORTANT
A triangle has two of its sides along the axis, its third side touches the circle x2+y2 2ax2ay+a2=0. Find the equation of the locus of the circumcentre of the triangle.
EASY
JEE Main
IMPORTANT
A straight line moves so that the algebraic sum of the perpendiculars drawn to it from two fixed points is constant. Show that the line always touches a fixed circle.