The tangents drawn from the origin to the circle x2 + y2 – 2kx – 2ry + r2 = 0 are perpendicular, if:
k = r
Equation of the circle is
∴ tangents are perpendicular coefficient of x2 + coefficient of y2 = 0
A circle passes through the point (–1, 7) and touches the line y = x at (1, 1). Its diameter is
Let ABCD be a quadrilateral with area 18, with side AB parallel to the side CD and AB = 2CD. Let AD be perpendicular to AB and CD. If a circle is drawn inside the quadrilateral ABCD touching all the sides, then its radius is
Let a circle be given by 2x(x – a) + y(2y – b) = 0, (a ≠ 0, b ≠ 0). Find the condition on a and b, if two chords each bisected by the x – axis can be drawn to the circle from
The equation of the locus of the mid points of the chords of the circle 4x2 + 4y2 – 12x + 4y + 1 = 0 that subtend an angle of at its centre is:
Find the radius of the smallest circle which touches the straight line 3x– y = 6 at (1, –3) and also touches the line y = x. complete up to one place of decimal.
Let S ≡ x2 + y2 + 2gx + 2fy + c = 0 be a given circle. find the locus of the foot of the perpendicular drawn from the origin upon any chord of S which subtends a right angle at the origin.
The normal 3x – 4y = 4 and 6x – 8y – 7 = 0 are tangents to the circle. Then its radius is:
The circle x2 + y2 + x + y = 0 and x2 + y2 + x – y = 0 intersect at the angle of:
Find the radical centre of the circles, x2 + y2 + 3x + 2y + 1 = 0, x2 + y2 – x + 6y + 5 = 0, x2 + y2 + 5x – 8y + 15 = 0
The locus of the mid points of a chord of the circles x2 + y2 = 4, which subtends a right angle at the origin is: