Circle · Mathematics · WB JEE

The equation of the circle which passes through the points of intersection of the circles $${x^2} + {y^2} - 6x = 0$$ and $${x^2} + {y^2} - 6y = 0$$, and has its centre at $$\left( {{3 \over 2},{3 \over 2}} \right)$$ is

The equation $$(x - {x_1})(x - {x_2}) + (y - {y_1})(y - {y_2}) = 0$$ represents a circle whose centre is

The circles $${x^2} + {y^2} + 6x + 6y = 0$$ and $${x^2} + {y^2} - 12x - 12y = 0$$

The locus of the centres of the circles which touch both the axes is given by

The equation of the chord of he circle $${x^2} + {y^2} - 4x = 0$$ whose midpoint is (1, 0) is

The circles x² + y² $$-$$ 10x + 16 = 0 and x² + y² = a² intersect at two distinct points if

For the two circles x² + y² = 16 and x² + y² $$-$$ 2y = 0 there is/are

The straight line x + y $$-$$ 1 = 0 meets the circle x² + y² $$-$$ 6x $$-$$ 8y = 0 at A and B. Then the equation of the circle of which AB is a diameter is

If the straight line y = mx lies outside of the circle x² + y² $$-$$ 20y + 90 = 0, then the value of m will satisfy

The locus of the centre of a circle which passes through two variable points (a, 0), ($$-$$a, 0) is

The intercept on the line y = x by the circle x² + y² $$-$$ 2x = 0 is AB. Equation of the circle with AB as diameter is

If the coordinates of one end of a diameter of the circle $${x^2} + {y^2} + 4x - 8y + 5 = 0$$ is (2, 1), the coordinates of the other end is

Chords $$\mathrm{AB}$$ & $$\mathrm{CD}$$ of a circle intersect at right angle at the point $$\mathrm{P}$$. If the length of AP, PB, CP, PD are 2, 6, 3, 4 units respectively, then the radius of the circle is

If two circles which pass through the points $$(0, a)$$ and $$(0,-a)$$ and touch the line $$\mathrm{y}=\mathrm{m} x+\mathrm{c}$$, cut orthogonally then

A curve passes through the point (3, 2) for which the segment of the tangent line contained between the co-ordinate axes is bisected at the point of contact. The equation of the curve is

If the equation of one tangent to the circle with centre at (2, $$-$$1) from the origin is 3x + y = 0, then the equation of the other tangent through the origin is

The side AB of $$\Delta$$ABC is fixed and is of length 2a unit. The vertex moves in the plane such that the vertical angle is always constant and is $$\alpha$$. Let x-axis be along AB and the origin be at A. Then the locus of the vertex is

Two circles $${S_1} = p{x^2} + p{y^2} + 2g'x + 2f'y + d = 0$$ and $${S_2} = {x^2} + {y^2} + 2gx + 2fy + d' = 0$$ have a common chord PQ. The equation of PQ is

A straight line meets the co-ordinate axes at A and B. A circle is circumscribed about the triangle OAB, O being the origin. If m and n are the distances of the tangent to the circle at the origin from the points A and B respectively, the diameter of the circle is

Twenty metres of wire is available to fence off a flower bed in the form of a circular sector. What must the radius of the circle be, if the area of the flower bed be greatest?