Question

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

Solution

Correct option is

c2 – 34c + 64 = 0

Let OAOB be the tangents from the origin to the given circle with centre C(–3, 5) and radius   

Then area of the quadrilateral OACB = 2 × area of the triangle OAC  

                           

Now OA = length of the tangent from the origin to the given circle   

  

SIMILAR QUESTIONS

Q1

If OA and OB are two equal chords of the circle x2 + y2 – 2x + 4y = 0 perpendicular to each other and passing through the origin O, the slopes of OA and OB are the roots of the equation 

Q2

An equation of the chord of the circle x2 + y2 = a2 passing through the point (2, 3) farthest from the centre is

Q3

The lengths of the intercepts made by any circle on the coordinates axes are equal if the centre lies on the line (s) represented by

Q4

A circle touches both the coordinates axes and the line  the coordinates of the centre of the circle can be

Q5

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

Q6

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   

 

Q7

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. 

Q8

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

Q9

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 =

Q10

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