Question

A chord of the circle x2 + y2 – 4x – 6y = 0 passing through the origin subtends an angle tan-1 (7/4) at the point where the circle meets positivey-axis.

Equation of the chord is

Solution

Correct option is

x – 2y = 0

The given circle passes through the origin O and meets the positive Y-axis at B(0, 6). Let OP be the chord of the circle passing through the origin subtending an angle θ at B, where

tan θ = 7/4   

  

Equation of the tangent OT at O to the given circle is  

                  2x + 3y = 0   

⇒           slope of the tangent = –2/3   

     

                                                                

 

  

Hence the equation of OP is y = x tan (θ – α) ⇒ x – 2y = 0

SIMILAR QUESTIONS

Q1

If the tangent at the point P on the circle x2 + y2 + 6x + 6y = 2 meets the straight line 5x – 2y + 6 = 0 at a point Q on the y-axis, then the length ofPQ is

Q2

If a > 2b > 0 then the positive value of m for which  is a common tangent to x2 + y2 = b2 and (x – a)2y2 = b2 is   

 

Q3

Let PQ  and RS be tangents at the extremities of a diameter PR of a circle of radius r. Such that PS and RQ intersect at a point X on the circumference of the circle, then diameter of the circle equals. 

Q4

A triangle PQR is inscribed in the circle x2 + y2 = 25. If Q and R have coordinates (3, 4) and (–4, 3) respectively, then QPR is equal to

Q5

For each natural number k, let Ck denote the circle with radius centimeters and centre at the origin O, on the circle Ck a particle moves k centimeters in the counter-clockwise direction. After completing its motion on Ck, the particle moves to Ck + 1 in the radial direction. The motion of the particle continues in this manner. The particle starts at (1, 0). If the particle crosses the positive direction of x-axis for the first time on the circle Cn then n =

Q6

If the area of the quadrilateral formed by the tangent from the origin to the circle x2 + y2 + 6x – 10y + c = 0 and the pair of radii at the points of contact of these tangents to the circle is 8 square units, then c is a root of the equation

Q7

If two distinct chords, drawn from the point (pq) on the circle x2 + y2px + qy (where pq  0) are bisected by the x-axis, then

Q8

Let A0 A1 A3 A4 A5 be a regular hexagon inscribed in a unit circle with centre at the origin. Then the product of the lengths of the line segmentsA0 A1A0 A2 and A0 A4 is

Q9

C1 and C2 are circles of unit radius with centres at (0, 0) and (1, 0) respectively. C3 is a circle of unit radius, passes through the centres of the circles C1 and C2 and have its centre above x-axis. Equation of the common tangent to C1 and C3 which does not pass through C2 is

Q10

On the line joining the points A (0, 4) and B (3, 0), a square ABCD is constructed on the side of the line away from the origin. Equation of the circle having centre at C and touching the axis of x is