Question

The angle between the tangents drawn from the origin to the circle (x – 7)2 + (y + 1)2 = 25 is

Solution

Correct option is

π/2

If y = mx is a tangent from the origin to the circle (x – 7)2 + (y + 1)2 = 25, then  

                

If m1m2 are its roots, then m1m2 = –12/12 = –1.   

Hence the angle between the two tangents is π/2.  

So, (c) is correct answer. (Here origin lies on director circle of given circle) 

SIMILAR QUESTIONS

Q1

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

 

Q2

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

Q3

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

Q4

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

Q5

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  

Q6

2:- Equations of the member of the family S which bisects the circumference of C is

Q7

3:- If O is the origin and P is the centre of C, then the difference of the squares of the lengths of the tangents from A and B to the circle is equal to

Q8

If the two (x – 1)2 + (y – 3)2 = r2 and x2 + y2 – 8x + 2y + 8 = 0 intersect in two distinct points, then

Q9

The distance between the chords of contact of the tangent to the circle x2 + y2 + 2gx + 2fy + c = 0 from the origin and the point (gf) is

Q10

A square is inscribed in the circle x2 + y2 – 2x + 4y + 3 = 0. Its sides are parallel to the co-ordinates axes. Then one vertex of the square is