Question

The length of the longest ray drawn from the point (4, 3) to the circle x2y2 + 16x + 18y + 1 = 0 is equal to

Solution

Correct option is

The radius of the circle 

 

Length of the longest ray is equal to the length of the tangent from the point (4, 3) which is    

  

SIMILAR QUESTIONS

Q1

The coordinates of two point P and Q are (2, 3) and (3, 2) respectively. Circles are described on OP and OQ as diameters; O being the origin, then length of the common chord is

Q2

The circle x2 + y2 – 6x – 4y + 9 = 0 bisects the circumference of the circle x2 + y2 – (λ + 4)x – (λ + 2)y + (5λ + 3) = 0 if λ is equal to

Q3

The locus of the middle points of the chords of the circle of radius which subtend an angle π/4 at any point on the circumference of the circle is a concentric circle with radius equal to

Q4

The lengths of the tangents from two points A and B to a circle are l and l’ respectively. If the points are conjugate with respect to the circle, then (AB)2 is equal to

Q5

If two circles, each of radius 5 units, touch each other at (1, 2) and the equation of their common tangent is 4x + 3y = 10, then equation of the circle, a portion of which lies in all the quadrants is

Q6

A point moves such that the sum of the squares of its distances from the sides of a square of side unity is equal to 9. The locus of such a point is a circle

Q7

Radical centre of the three circles x2 + y2 = 9, x2 + y2 – 2x – 2y = 5, x2 + y2 + 4x + 6y = 19 lies on the line y = mx if m is equal to

 

Q8

The coordinates of the point on the circle x2 + y2 – 2x – 4y – 11 = 0 farthest from the origin are 

Q9

A circle passes through the origin O and cuts the axis at A(a, 0) and B(0,b). The reflection of O in the line AB is the point

Q10

1:- The chords in which the circle C cuts the members of the family S of circles through A and B are con-current at