## Question

### Solution

Correct option is Equation of any circle through (0, 0) and (1, 0) is  If it represents C3, its radius = 1  As the centre of C3, lies above the x-axis, we take and thus an equation of C3 is . Since C1 and C3 intersect and are of unit radius, their common tangents are parallel to the line joining their centres (0, 0) and So, let the equation of a common tangent be It will touch C1, if From the figure, we observe that the required tangent makes positive intercept on the y-axis and negative on the x-axis and hence its equation is #### SIMILAR QUESTIONS

Q1

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

Q2

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

Q3

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

Q4

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.

Q5

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

Q6

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 =

Q7

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

Q8

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

Q9

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

Q10

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