JEE 2020 Mathematics : Circle - 02 (04.09.2019)

The tangents are drawn from the point (4, 5) to the circle x² +y² – 4x – 2y – 11 = 0 . The area of quadrilateral formed by these tangents and radii, is

The angle between a pair of tangents drawn from a point P to the circle x² + y² + 4x – 6y + 9  is . The equation of the locus of the point P is

If a straight line through making an angle of 135^o with the x-axis cuts the circle x = 5 cos θ, y = 5 sinθ at points A and B, then the length of AB is

The number of common tangents to the circles x² + y² = 9 and x² + y² + 6x – 8y = 24 is

If is a chord of the circle , then the equation of the circle of which this chord is a diameter, is

If the straight line  touches the circle  and is normal to the circle , then the values of a and b are respectively

If the tangent at the point P on the circle  meets the straight line  at a point Q on the y- axis, then the length of PQ is

If the length of the tangents drawn from the point (1,2) to the circles and  be in the ratio 4: 3, then k =

If a circle C passing through (4, 0) touches the circle x² + y² 4x – 6y – 12 = 0 externally at a point (1, -1) then the radius of the circle C is :

If the tangent to the circle x² + y² = 5 at the point (1, -2) also touches the circle x² + y² – 8x + 6y + 20 = 0, then its point of contact is