Circle and Syst...

If the lines 2x - 3y = 5 and 3x - 4y = 7 are two diameters of a circle of radius 7, then the equation of the circle is

The circle x² + y² - 4x - 4y + 4 = 0 is inscribed in a triangle which has two of its sides along the coordinate axes. If the locus of the circumcentre of the triangle is x + y - xy + k √(x² + y²) = 0, then the value of k is

If one end of the diameter is (1, 1) and the other end lies on the line x + y = 3, then locus of centre of circle is

The equation of the smallest circle passing through the points (2, 2) and (3, 3) is

The equation (x - x₁) (x - x₂) + (y - y₁) ( y - y₂) = 0 represents a circle whose centre is

The center of the circle whose normals are x² - 2xy - 3x + 6y = 0, is

The equation of the circle with center (2, 1) and touching the line 3x + 4y = 5 is

If 2x - 4y = 9 and 6x - 12y + 7 = 0 are common tangents to the circle, then radius of circle is

If P(x₁, y₁) and Q(x₂, y₂) are two pints such that their abscissae x₁ and x₂ are the roots of the equation x² + 2x - 3 = 0 while the ordinates y₁ and y₂ are the roots of the equation y² + 4y - 12 = 0. Then, the centre of the circle wit PQ as diameter is

The locus of the centre of the circle for which one end of a diameter is (1, 1) while the other end is in the line x + y = 3 is