Question

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

Solution

Correct option is

5

The line 5x – 2y + 6 = 0 meets y-axis at (0, 3). So the coordinates of Qare (0, 3) and PQ is the length of the tangent from Q (0, 3) to the circlex2 + y2 + 6x + 6y – 2 = 0. Hence

         

SIMILAR QUESTIONS

Q1

A line is drawn through the point P(3, 11) to cut the circle x2 + y2 = 9 at A and B. Then PAPB is equal to

Q2

Two rods of lengths a and b slide along the x-axid and y-axis respectively in such a manner that their ends are concyclic. The locus of the centre of the circle passing through the end points is

Q3

If the point (1, 4) lies inside the circle x2 + y2 – 6x – 10y + p = 0 and the circle does not touch or interest the coordinates axes, then

Q4

If the line x cos α + y sin α = p represents the common chord APQB of the circle x2 + y2 = a2 and x2 + y2 = b2 (a > b) as shown in the Fig, then AP is equal to

Q5

Two points P and Q are taken on the line joining the points A (0, 0) and B (3a, 0) such that AP = PQ = QB. Circles are drawn onAPPQ, and QB as diameters. The locus of the point S, the sum of the squares of the lengths of the tangents from which to the three circles is equal to b2, is

Q6

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 

Q7

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

Q8

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

Q9

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

Q10

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