Frequent Circle Questions

a square is inscribed in a circle x2+y2-2x+4y+3=0, whose sides are parallel to the coordinates axes one vertex of the square is? ...

Find the locus of the midpoint of the chord of the circle x^2 + y^2 = a^2 which subtends a 90° angle at point (p,q) lying inside the circle. ...

THE CIRCLE X2+Y2-4X-8Y+16=0 rolls up the tangent to it at (2+√3 , 3) by 2 units , assuming the x axis as horizontal , find the equation of the circle in the new position- ...

prove that the polars of any point with respect to a system of coaxal circles all pass through a fixed point and that the two points are equidistant from the radical axis and subtend a right angle at a limiting point of the s ...

if x2+y2=a2 then equation of tangent which: 1. passes through (b,0) 2.makes an area of a2 with the coordinate axes ...

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The chord of contact of the pair of tangents drawn from each point on the line 2x+y=4 to the circle {{x}^{2}}+{{y}^{2}}=1 pass through the point a) (1/2, – 1/4) b) (1/2, 1/4) c) (– 1/2, 1/4) d) (– 1/2, – 1/4) ...

The tangent at a point C of a circle and diameter AB when extended intersect at P. If ∠PCA = 110° , find ∠CBA. a) 70° b) 105° c) 110° d) 120° ...

The equation of the circle passing through the points (0, 0),(0,b) and (a,b) is a) {{x}^{2}}+{{y}^{2}}+ax+by=0 b) {{x}^{2}}+{{y}^{2}}-ax+by=0 c) {{x}^{2}}+{{y}^{2}}+x+3y=0 d) {{x}^{2}}+{{y}^{2}}+ax-by=0 ...

The normal at the point (3, 4) on a circle cuts the circle at the point ( –1, –2). Then the equation of the circle is ...

If a circle, whose centre is (–1, 1) touches the straight line x + 2y + 12 = 0, then the coordinates of the point of contact are ...

If the lines 3x - 4y + 4 = 0 and 6x - 8y - 7 = 0 are tangents to a circle, then the radius of the circle is ...

If the radical axis of circles {{x}^{2}}+{{y}^{2}}-6x-8y+p=0 and {{x}^{2}}+{{y}^{2}}-8x-6y+14=0 passes through the point (1, – 1), then p is equal to ...

The locus of the centre of circle which cuts the circles {{x}^{2}}+{{y}^{2}}+4x-6y+9=0 and {{x}^{2}}+{{y}^{2}}-4x+6y+4=0 orthogonally is ...