Circle questions
490 published questions with worked solutions.
- Let the centre of a circle C be ( , ) and its radius r < 8. Let 3x + 4y = 24 and 3x – 4y = 32 be two tangents and 4x + 3y = 1 be...
- Let w = z z+k_1z+k_2iz+ (1+i), k_1, k_2 R. Let Re(w) = 0 be the circle C of radius 1 in the first quadrant touching the line y =...
- The number of common tangents, to the circles x^2+y^2-18x-15y+131=0 and x^2+y^2-6x-6y-7=0, is
- Points P(–3, 2), Q(9, 10) and R( , 4) lie on a circle C with PR as its diameter. The tangents to C at the points Q and R...
- The points of intersection of the line ax + by = 0, (a ) and the circle x^2+y^2-2x=0 are A( , 0) and B(1, ). The image of the...
- A circle with centre (2, 3) and radius 4 intersects the line x + y = 3 at the points P and Q. If the tangents at P and Q...
- Let the tangents at the points A(4, –11) and B(8, –5) on the circle x^2+y^2-3x+10y-15=0, intersect at the point C. Then the...
- Let A be a point on the x-axis. Common tangents are drawn from A to the curves x^2+y^2=8 and y^2=16x. If one of these tangent...
- Let y = x + 2, 4y = 3x + 6 and 3y = 4x + 1 be three tangent lines to the circle (x-h)^2+(y-k)^2=r^2. Then h + k is equal to
- Let a circle C_1 be obtained on rolling the circle x^2+y^2-4x-6y+11=0 upwards 4 units on the tangent T to it at the point (3,2)....
- Tangents are drawn from the point (17, 7) to the circle x^2 + y^2 = 169. STATEMENT-1 : The tangents are mutually perpendicular....
- Consider L_1 : 2x + 3y + p - 3 = 0 L_2 : 2x + 3y + p + 3 = 0, where p is a real number, and C : x^2 + y^2 + 6x - 10y + 30 = 0....
- Tangents drawn from the point P(1, 8) to the circle x^2 + y^2 - 6x - 4y - 11 = 0 touch the circle at the points A and B. The...
- The centres of two circles C_1 and C_2 each of unit radius are at a distance of 6 units from each other. Let P be the mid point...
- If the chord y = mx + 1 of the circle x^2 + y^2 = 1 subtends an angle of measure 45^0 at the major segment of the circle then...
- The centre of the circle passing through (0, 0) and (1, 0) and touching the circle x^2 + y^2 = 9 is
- If the two circles (x - 1)^2 + (y - 3)^2 = r^2 and x^2 + y^2 - 8x + 2y + 8 = 0 intersect in two distinct point, then
- The lines 2x - 3y = 5 and 3x - 4y = 7 are diameters of a circle having area as 154 sq. units. Then the equation of the circle is
- If the lines 2x + 3y + 1 = 0 and 3x - y - 4 = 0 lie along diameters of a circle of circumference 10 , then the equation of the...
- The intercept on the line y = x by the circle x^2 + y^2 - 2x = 0 is AB. Equation of the circle on AB as a diameter is
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